# How do you find the critical points of f(x)=(x-10)^2(x+5)?

Apr 25, 2018

$x = 0 , x = 10$ are criticial points

#### Explanation:

As implied by the subtitle of this section, the critical points are those at which the first derivative of an expression are equal to zero.

f(x) = (x−10)^2(x+5) First, let's expand this:
f(x) = (x^2 −20x +100)(x+5)
f(x) = x^3 −20x^2 +100x + 5x^2 − 100x +500
f(x) = x^3 − 15x^2 + 500 NOW we can find the derivative:

$f ' \left(x\right) = 3 {x}^{2} - 30 x = 0$ are the critical points.
$x = 0 , x = 10$ are criticial points