Chapter 3: Q. 92 (page 277)
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Sketch careful, labeled graphs of each function f in Exercises 63–82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of and examine any relevant limits so that you can describe all key points and behaviors of f.
Use the first derivative test to determine the local extrema of each function in Exercises 39- 50. Then verify your algebraic answers with graphs from a calculator or graphing utility.
Determine whether or not each function f in Exercises 53–60 satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b]. For those that do, use derivatives and algebra to find the exact values of all c ∈ (a, b) that satisfy the conclusion of the Mean Value Theorem.
Find the possibility graph of its derivative f'.
The cost of manufacturing a container for frozen orange juice is cents, where is the height of the container in inches. Your boss claims that the containers will be the cheapest to make if they are inches tall. Use Theorem 3.3 to quickly show that he is wrong.
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