Let f be a function that is differentiable at all points of the interval [0, 1] and let 0

Let f be a function that is differentiable at all points of the interval [0, 1] and let 0 < c < 1. Prove that if f has a local maximum value at c and c is not a critical point of g then f + g does not have a local maximum value at c. Let f be a function that is differentiable at all points of the interval [0, 1] and let 0 < c < 1. Prove that if f has a local maximum value at c and c is not a critical point of g then f + g does not have a local maximum value at c.