Question

What are the critical numbers of `f(x) = x^2*(1 + 3 ln x)`?

Answer 1

The only critical number is `x = e^(-5/6)`

Explanation:

`f'(x) = 2x(1+3lnx)+x^2(3/x)= x(6lnx+5)`

`f'(x)` is defined for all `x` in the domain of `f` and

`f'(x)=0` at `lnx = -5/6` so `x = e^(-5/6)`.