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Chapter 3: Q. 41 (page 311)
Calculate each of the limits in Exercises 15鈥�20 (a) using
L鈥橦opital鈥檚 rule and (b) without using L鈥橦 藛 opital鈥檚 rule.
a
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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.
Sketch careful, labeled graphs of each function f in Exercises 63鈥�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.
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 point.
Prove that the function is increasing on all values of real numbers.
.
Sketch the graph of a function f with the following properties:
f is continuous and defined on R;
f(0) = 5;
f(鈭�2) = 鈭�3 and f '(鈭�2) = 0;
f '(1) does not exist;
f' is positive only on (鈭�2, 1).
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