AP Calculus Warm up 9.3.14 What is the derivative of a function? The derivative of a function is also a function which gives us the instantaneous rate of change (or slope) of the curve at any given point.
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1. AP Calculus Warm up 9.3.14 What is the derivative of a
function? The derivative of a function is also a function which
gives us the instantaneous rate of change (or slope) of the curve
at any given point.
2. And now its time for.. The Lame Joke of the day.. What did
the turkey say to the computer? Google, Google, Google.
3. AP Calculus Warm up 9.3.14 What is the derivative of a
function? The derivative of a function is also a function which
gives us the instantaneous rate of change (or slope) of the curve
at any given point.
4. Secant line = Average rate of change
5. The secant line becomes the tangent line
6. Tangent line = instantaneous rate of change.
7. Rates of change Average rate of change slope of secant line
Use slope formula Instantaneous rate of change slope of Tangent
line Use derivative
8. A beaker is being heated continuously over time (t) and is
modeled by the twice differentiable function C (t). The table above
gives selected values of the temperature in degrees Celsius.
Estimate the instantaneous rate of change of the temperature at 14
minutes. Indicate units of measure. Time (t) minutes 0 2 9 20 35
Temperature C (t) in degrees Celsius 60 63 89 102 110
9. Find the Instantaneous Rate of change at (2, 12) f (x)
3x2
10. What is the equation of the tangent line of f(x) at ( 2,
12) Slope = 12 f (x) 3x2
11. Differentiation The process of finding the derivative of a
function If a function has a derivative, it is called
differentiable
12. What makes a function differentiable? 1. It MUST be
continuous. 2. The derivative from the left must equal the
derivative from the right.
13. Most common times when a derivative does not exist. 1. At a
sharp corner 2. At a vertical tangent line or asymptote
14. KEY POINT Differentiability implies continuity, But
continuity DOES NOT imply differentiability.
15. Notation
16. Review The derivative of a function is also a function
which gives us the instantaneous rate of change (or slope) of the
curve at any given point.
17. The graph of f is given below. Sketch out the graph of
f