Question

What are the critical values, if any, of `f(x) = lnx^2+xlnx-x^2`?

Answer 1

x = 1.385

Explanation:

`f(x) = lnx^2+xlnx-x^2`

`f'(x) =color{red}{ 1/x^2 * 2x} + color{green}{(lnx + x * 1/x)} - color{blue}{ 2x}`

where
red = chain rule
green = product rule
blue = power rule

`= 2/x + lnx + 1 - 2x= 0`

i "solved" this by a Desmos plot