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Chapter 3: Q. 61 (page 311)
Calculate each of the limits in Exercises 49–64. Some of these limits are made easier by considering the logarithm of the limit first, and some are not.
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Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points.
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 .)
Sketch the graph of a function f with the following properties:
f is continuous and defined on R;
f has critical points at x = −3, 0, and 5;
f has inflection points at x = −3, −1, and 2.
For each set of sign charts in Exercises 53–62, sketch a possible graph of f.
Determine whether or not each function satisfies the hypotheses of the Mean Value Theorem on the given interval . For those that do, use derivatives and algebra to find the exact values of all that satisfy the conclusion of the Mean Value Theorem.
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