Question

Let \[c\] be a critical point of a continuous function \[f\]. If \[f'(x)\] changes sign from negative to positive as \[x\] passes through \[c\], what is \[c\]?

Options

• a point of local minimum

• a point of local maximum

• an absolute maximum

• a point of inflection

Answer 1

A negative derivative means the function is decreasing, and a positive derivative means it is increasing. This negative-to-positive change gives a point of local minimum at \[c\].