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Magazine Chapter 3: Q. 91 (page 277)
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Chapter 3: Q. 91 (page 277)
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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.
Find the possibility graph of its derivative f'.
For the graph of f in the given figure, approximate all the values x 鈭� (0, 4) for which the derivative of f is zero or does not exist. Indicate whether f has a local maximum, minimum, or neither at each of these critical points.
Find the possibility graph of its derivative f'.
Last night at 6 p.m., Linda got up from her blue easy chair. She did not return to her easy chair until she sat down again at 8 p.m. Let s(t) be the distance between Linda and her easy chair t minutes after 6 p.m. last night.
(a) Sketch a possible graph of s(t), and describe what Linda did between 6 p.m. and 8 p.m. according to your graph. (Questions to think about: Will Linda necessarily move in a continuous and differentiable way? What are good ranges for t and s?
(b) Use Rolle鈥檚 Theorem to show that at some point between 6 p.m. and 8 p.m., Linda鈥檚 velocity v(t) with respect to the easy chair was zero. Find such a place on the graph of s(t).
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