Question

For \[f'(x)=12(x-3)(x+2)\], what is the nature of \[f\] on \[(-2,3)\]?

Options

• \[f\] is strictly increasing on \[\mathbf{R}\].

• \[f\] is decreasing.

• \[f\] is increasing.

• \[f\] is constant.

Answer 1

On \[(-2,3)\], the factors \[x-3\] and \[x+2\] have opposite signs, so \[f'(x)<0\]. A negative derivative means \[f\] is decreasing.