Let f be a differentiable function defined on the closed interval [a,b] and let c be a point in the open interval (a,b) such that

Question

I.f'(c)=0

II.f'(x)>0 when a≤x<c

III.f'(x)<0 when c<x<≤b

Which of the following statements must be true?

(A)f(c)=0

(B)f"(c)=0

(C)f(c) is an absolute maximum value of f on [a,b]

(D)f(c) is an absolute minimum value of f on [a,b]

(E)f(x) has a point of inflection at x=c

Answer 1

Consider the function y = -x^2