If g is a differentiable function and g(0)=0 and g'(0) > 0. a) Prove that f(x) = 1/2 (integral from 1 to x) (x-t)g(t)dt f is differentiable. b) f has a local minimum at x=0 by using the definition of f

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If g is a differentiable function and g(0)=0 and g'(0) > 0. a) Prove that f(x) = 1/2 (integral from 1 to x) (x-t)g(t)dt f is differentiable. b) f has a local minimum at x=0 by using the definition of f.
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