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Chapter 3: Q. 30 (page 314)
L鈥橦藛opital鈥檚 Rule limit calculations: Calculate each of the
limits that follow. Some of these limits are easier to calculate
by using L鈥橦opital鈥檚 rule, and some are not.
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For the graph of f in the given figure , approximate all the values x 鈭� (0, 4) for which the derivative of f is zero or does not exist. Indicate whether f has a local maximum, minimum, or neither at each of these critical points .
Use a sign chart for to determine the intervals on which each function is increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.
Determine whether or not each function f in Exercises 53鈥�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 鈭� (a, b) that satisfy the conclusion of the Mean Value Theorem.
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.
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.
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