Let f (x) and g(x) be differentiable functions in (a, continuous at a and b, and g(x) #0 in [a, b]. Then prove th g(a) f(b)-f(a)g(b) _ (b-a) g(a) g (b) for at least o = g(c) f'(c) - f(c) g'(c) (ale))²

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A: As per our guidelines we can answer only 3 subparts. please ask others seperately.

Q: 3. Let there be some a, b R such that f(a)ƒ'(a) = f(b)ƒ'(b) + 1. Show that f f(x) f"(x)dx ≤ 1.

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