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# c1-t3 - NAME TEST3/MAC2311 Page 1 of 5 Read Me First Show...

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NAME: TEST3/MAC2311 Page 1 of 5 ______________________________________________________________________ Read Me First: Show all essential work very neatly. Use correct notation when presenting your computations and arguments. Write using complete sentences. Be careful. Remember this: "=" denotes "equals" , " " denotes "implies" , and " " denotes "is equivalent to". Do not "box" your answers. Communicate. Show me all the magic on the page. Eschew obfuscation. ______________________________________________________________________ 1. (10 pts.) Write down each of the following derivatives. [2 pts/part.] (a) (b) (c) (d) (e) ______________________________________________________________________ 2. (10 pts.) (a) Use logarithmic differentiation to find dy / dx when (b) Find dy / dx when

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TEST3/MAC2311 Page 2 of 5 ______________________________________________________________________ 3. (10 pts.) (a) (6 pts.) Find formulas for y and the differential dy when y = x 2 . Label your expressions correctly. (b) (4 pts.) Use an appropriate local linear approximation formula to estimate . . ______________________________________________________________________ 4. (10 pts.) (a) Let . Show that f is one-to-one on (0, ) using f . [A little explanation is needed!] (b) Let , where f is from part (a) of this problem. Compute . Hint: f (2) = ??
TEST3/MAC2311 Page 3 of 5 ______________________________________________________________________ 5. (10 pts.) Fill in the blanks appropriately. [ DEFINITIONS!!! ] (a) A function f has a relative minimum at x 0

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c1-t3 - NAME TEST3/MAC2311 Page 1 of 5 Read Me First Show...

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