Question:
The minimum value
1. Let I be an interval in R and assume f : I→R is twice differentiable at all points of I. Suppose that a∈I, f'(a) = 0 and f'(x)≠0 for all x∈I, x≠a. Prove: If f"(a) > 0, then f(c) is the minimum value of f in I; that is f(c)≤f(x) for all x∈I.