Question

Find the inflection points. Find the interval on which f is concave up. Find the interval on which f is concave down. Step 1 We have f'(x) = 4 cos(x) – 4 sin(x), so f"(x) = -4 cos (x) – 4 sin (x) - 4 sin(x) – 4 cos(x) which equals 0 when tan(x) = -1 Hence, in the Interval o <x< 211, f'(x) = 0 77 when X = 371 4 7 л 4 and x = Step 2 When x 3. f"(x) is negative negative, and f(x) is concave down down Step 3 When Зл 4 << f"(x) is positive positive, and f(x) is concave up up. Step 4 When 710 1<x< 21, "(x) is negative 4 negative, and f(x) is concave down down

Answer 1

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