Question

If a differentiable function has an absolute max or min at an interior point \[c\], what must be true?

Options

• \[f(c)=0\]

• \[f'(c)=1\]

• \[f\] is not differentiable at \[c\]

• \[f'(c)=0\]

Answer 1

At an interior absolute extremum of a differentiable function, the derivative must be zero. Therefore, \[f'(c)=0\].