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

1 Answer
Apr 25, 2018

Answer:

#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