What are the extrema of x^3-2x^2-8x?

Dec 23, 2015

$\frac{2 + 2 \sqrt{7}}{3} \mathmr{and} \frac{2 - 2 \sqrt{7}}{3}$

Explanation:

$f \left(x\right) = {x}^{3} - 2 {x}^{2} - 8 x$
$f ' \left(x\right) = 3 {x}^{2} - 4 x - 8$
$3 {x}^{2} - 4 x - 8 = 0$

since this is not factorable we use the quadratic equation

$x = \frac{2 + 2 \sqrt{7}}{3}$