Question

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

Answer 1

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

Explanation:

`f'(x)=3*x^2+2*3x=3x^2+6x=0`

This can be factorised:
`->3*x*(x+2)=0`
`->x=0orx=-2`

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