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Chapter 3: Q. 31 (page 311)
Calculate each of the limits in Exercises 21-48. Some of these limits are made easier by L'Hôpital's rule, and some are not.
The value of limit is zero
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Find the possibility graph of its derivative f'.
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.
For each set of sign charts in Exercises 53–62, sketch a possible graph of f.
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.
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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