A function f(x) is continuous for all x and has a local minimum at (1,8). Which must be true?

Question

A. f'(1)=0
B. f' exists at x=1
C. The graph is concave up at x=1
D. f'(x) is less than 0 if x is less than 1, f'(x) is greater than 0 if x is greater than 1
E. f'(x) is greater than 0 if x is less than 1, f'(x) is less than 0 if x is greater than 1

I got A but I'm not sure. Thanks.

Answer 1

D

Consider the function

y = |sin(x-1)|