Question

What are the critical values, if any, of `f(x)= x^2*(1 + 3 ln x)`?

Answer 1

To find critical values, we just have to set `f'(x) = 0`

Explanation:

`f(x) = x^2*(1 + 3 ln x)`

`implies f'(x) = 2x*(1+3lnx) + (x^2) * (3/x)`
`implies f'(x) = 2x*(1+3lnx) + 3x`
`implies f'(x) = 0`
`implies 2x*(1+3lnx) + 3x =0`
`implies x(2*(1+3lnx) + 3) = 0`
`implies x = 0` or `(2*(1+3lnx) + 3)=0`
`implies x=0` or `x=e^(-5/6)`