Question

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

Options

• an absolute minimum

• a point of local maximum

• a point of inflection

• a point of local minimum

Answer 1

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