Suppose that f has continuous derivative and is twice differentiable in R. Suppose that f(a) = f(b) = = 0. Show that for every x E (a, b), there is E (a, b) such that f"(£), (x – a) (x – 6). f(æ) = 2...

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Extracted text: Suppose that f has continuous derivative and is twice differentiable in R. Suppose that f(a) = f(b) = = 0. Show that for every x E (a, b), there is E (a, b) such that f"(£), (x – a) (x – 6). f(æ) = 2 Hint: let k = f(x)/(x – a)(x – b); consider the function F(t) = f(t) – k(x – a)(x – b) and use the first exercise.