Question: Do the following for each function f (x). (a) Find f'(x) and f(x). (b) Graph f(x), f'(x), and f(x) with a graphing utility. (c) Identify
(a) Find f'(x) and f"(x).
(b) Graph f(x), f'(x), and f"(x) with a graphing utility.
(c) Identify x-values where f"(x) = 0, f"(x) > 0, and f"(x) < 0.
(d) Identify x-values where f'(x) has a maximum point or a minimum point, where f'(x) is increasing, and where f'(x) is decreasing.
(e) When f(x) has a maximum point, is f"(x) > 0 or f"(x) < 0?
(f) When f(x) has a minimum point, is f"(x) > 0 or f"(x) < 0?
f(x) = x3 - 3x2 + 5
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