Determine whether the statement is true or false. Explain why.

Question

a) If f'(c)=0, then f has a local maximum,minimum at c

b) If f has an absolute minimum value at c, then f'(c)=0

c)If f''(2)=0, then (2,f(2)) is an inflection point on the curve y=f(x)

Answer 1

Hello Robert H., Here are some clues.

a) Look at f(x) = x^3 at x = 0.

b) Look at f(x) = absolute value of x at x = 0.

c) Look at f(x) = 5.

Tom S.