Question

How do you find the critical points of f when `f(x)= x^4/(5(x-5)^2)`?

Answer 1

Critical points are x=0, x= 10

First get f'(x)= `1/5[(4x^3 (x-5)^2 - x^4 2(x-5))/(x-5)^4]`

`(2x^3 (x-5))/5[(2(x-5)-x)/(x-5)^4]`

`(2x^3) /5(x-10)/(x-5)^3`

Solving for f(x)=0, it is x=0, x=10

At x=5, f'(x) does not exist, hence x=5 is also a critical point.