Question: Show that if f has a continuous second derivative on [a, b] and f'(a) = f'(b) = 0, then x f(x) dx = f(a) f(b).

Show that if f has a continuous second derivative on [a, b] and f'(a) = f'(b) = 0, then

x f

x f"(x) dx = f(a) f(b).

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