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Page 1: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 2: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 3: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 4: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 5: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 6: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 7: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 8: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 9: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 10: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 11: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 12: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 13: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 14: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 15: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 16: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 17: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 18: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 19: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 20: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 21: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 22: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 23: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 24: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 25: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 26: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 27: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 28: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 29: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 30: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 31: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 32: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 33: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 34: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 35: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 36: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 37: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 38: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 39: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 40: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 41: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 42: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 43: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 44: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 45: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 46: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 47: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 48: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 49: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 50: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 51: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 52: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 53: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 54: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 55: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 56: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 57: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 58: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 59: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 60: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 61: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 62: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 63: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 64: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 65: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 66: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 67: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 68: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 69: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 70: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 71: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 72: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 73: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 74: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 75: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 76: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 77: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 78: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 79: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 80: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 81: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 82: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 83: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 84: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 85: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 86: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 87: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 88: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 89: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 90: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 91: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 92: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 93: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 94: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 95: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 96: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 97: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 98: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable
Page 99: Units 1 - 4efpub.spd.louisville.edu/classes/201/docs/ENGR201-Unit-04.pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers. Suppose f (x, y, z) and g(x, y, z) are differentiable

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