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Chapter 3: Q. 90 (page 312)
In your own words, prove the special case of L鈥橦opital鈥檚 藛
rule that is proved in the reading. Explain each step in
detail.
The special case of L鈥橦opital鈥檚 藛 rule is proved
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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.
Find the critical points of 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.
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.
For each set of sign charts in Exercises 53鈥�62, sketch a possible graph of f.
Find the critical points of the function
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