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Chapter 3: Q. 23 (page 310)
Calculate each of the limits in Exercises 21鈥�48. Some of these limits are made easier by L鈥橦opital鈥檚 rule, and some are not
The value of
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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.
Use the definition of the derivative to find f' for each function f.
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.
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.
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Use the second-derivative test to determine the local extrema of each function in Exercises . If the second-derivative test fails, you may use the first-derivative test. Then verify your algebraic answers with graphs from a calculator or graphing utility. (Note: These are the same functions that you examined with the first-derivative test in Exercises of Section .)
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