Calculus check

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

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asked by Anonymous
  1. D

    Consider the function

    y = |sin(x-1)|

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    posted by Steve

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