F-C4 NAME: Consider !(#) = −2#( + 18# − 28

1. Is !(#) continuous on the interval [5,9]? Explain.

2. Explain why there must be a value c in [5,9] such that !(,) = 8

3. Find the value or values of c in [5,9] such that !(,) = 8 guaranteed to exist in problem 2. D-C1

4. Use the limit definition of derivative to show that if !(#) = 2#( − 3# + 5, then !/(#) = 4# − 3.

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D-C7 For each problem, find the derivative function.

5. 1 = −3#2 − 9#4 + 5(4 #6 + 2

6. !(#) = 4#( − 6√89: + 5√#(;

7. 1 = (8 + √# −5(8<

8. 1 = =6

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F-L1a: Evaluate each limit

9. lim8→2

(8B4

10. lim8→(

(C86C89

F-L2a: Use the graph to rate each as true or false. If false, explain why. 11. lim

8→D!(#) = 3

12. lim

8→5!(#) = 1

13. lim

8→C5C!(#) = 3

14. lim

8→C5!(#) = 3

F-C3 15. Find and classify any discontinuities of the function. Justify your classifications using limits. !(#) = 8B44C68C89 F-B1: 16. Find any vertical and horizontal asymptotes of the function. Justify your answer with limits. !(#) = (8C28B4

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