Question

For \[f(x)=4x^3-6x^2-72x+30\], on which intervals is \[f\] increasing?

Options

• \[(-\infty,-2)\] and \[(3,\infty)\]

• \[(-2,3)\] only

• \[\mathbf{R}\]

• \[(-\infty,3)\] only

Answer 1

The derivative \[f'(x)=12(x-3)(x+2)\] is positive on \[(-\infty,-2)\] and \[(3,\infty)\]. Therefore \[f\] is increasing on both intervals.