Question

Which statement about \[f'(x)=0\] and constant behaviour is correct?

Options

• \[f'(x)=0\] at one point makes the function strictly increasing.

• \[f'(x)=0\] at one point makes the function strictly decreasing.

• A single point where \[f'(x)=0\] does not necessarily make the function constant.

• A single point where \[f'(x)=0\] makes the function constant on its entire domain.

Answer 1

Constant behaviour requires \[f'(x)=0\] throughout an interval. A derivative equal to zero at only one point is not sufficient to make a function constant.