73. Let f be differentiable at every value of x and suppose that f(1) = 1, that f' < 0 on (-x, 1), and that f' > 0 on (1, o). a. Show that f(x) > 1 for all x. b. Must f'(1) = 0? Explain.

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73. Let f be differentiable at every value of x and suppose that
f(1) = 1, that f' < 0 on (-x, 1), and that f' > 0 on (1, o).
a. Show that f(x) > 1 for all x.
b. Must f'(1) = 0? Explain.
Transcribed Image Text:73. Let f be differentiable at every value of x and suppose that f(1) = 1, that f' < 0 on (-x, 1), and that f' > 0 on (1, o). a. Show that f(x) > 1 for all x. b. Must f'(1) = 0? Explain.
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