Question

Consider the function, f x( ) = 2x3 −24x2 −7. Find the intervals of x where f(x) is increasing or decreasing.

Answer 1

$\frac{df}{dx}=6x^2-48x=6x(x-8).$

$\frac{df}{dx}>0 \to x<0\; or\; x>8$.

Thus, $f(x)$ increases on $(-\infin,0)\cup(8,\infin).$

$\frac{df}{dx}<0 \to 0<x<8.$

Thus, $f(x)$ decreases on $(0,8).$