# How do you find the relative extrema of the function f (x) = x^3 + 6 x^2?

Aug 6, 2015

Extrema is where the slope is zero. You find them by setting the derivative to zero.

#### Explanation:

$f ' \left(x\right) = 3 \cdot {x}^{2} + 2 \cdot 3 x = 3 {x}^{2} + 6 x = 0$

This can be factorised:
$\to 3 \cdot x \cdot \left(x + 2\right) = 0$
$\to x = 0 \mathmr{and} x = - 2$

You can feed this to the $f \left(x\right)$ function to get the corresponding values.
graph{x^3+6x^2 [-38.42, 43.75, -6.87, 34.25]}