1. The problem statement, all variables and given/known data 1) Prove that if f is an even function and is differentiable on R then the equation f'(x)=0 has at least a solution in R. 2) Conclude that if f is an even and differentiable function on R and f' is continuous at 0 than f'(0)=0. 3. The attempt at a solution 1)We know that f is an even function so that means that f(x)=f(-x) and it's differentiable on R. So that means that there exists either an Mam or a min value in R such that f'(m)=0 or f'(M)=0, and by substituting x for m we get f'(x)=0. 2)We know that f is even and differentiable on R so f has an axis of symmetry or a point of symmetry at the point 0. So f'(0)=0. Can someone tell me if this correct? If not what can i do to fix it. Thank you .