Given ##f(x)=3x^5-5x^3##, find all critical points.

[angela107]

Homework Statement

Given $f(x)=3x^5-5x^3$, find all critical points and identify any local
max/min point.

Relevant Equations

n/a

Is my work right?

 

[haruspex]

Check your factorisation of y'' (but you do not seem to have used it).
Other than that, looks fine.

 

[LuccaP4]

I think it's fine, but I agree with @haruspex that you have to check the factorisation of $y''$.
Just a friendly reminder: there are critical points as well where the derivative doesn't exist. In this case, the first derivative exists for every $x$, so you don't have to matter.