Question

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

Answer 1

`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'(x) = 3x^2 - 30x = 0` are the critical points.
`x = 0, x = 10` are criticial points