Question

What are the critical values of `f(x)=x^2-6x^3`?

Answer 1

Definition: `x=c` is a critical point of the function `f(x)` if
1st `f(c)` exists
AND
`f'(c)=0` or `f'(c)` does not exist

Now we have that

`f'(x)=2x-18x^2=>f'(x)=2x(1-9x)=>f'(x)=0=>x=0 or x=1/9`

Hence `f(0)=0` it exists so it is a critical value

and

`f(1/9)=1/243` it exists so it is a critical value