How do you find the critical numbers for $f(x)= x^(-8) ln x$ to determine the maximum and minimum?

Question

4029 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-22T18:09:08

The function has no critical numbers.

A critical number for $f$ is a number $c$ in he domain of $f$ where $f'(c) = 0$ or $f'(c)$ does not exist.

$f(x) = x^-8 = 1/x^8$ has domain: all reals except $0$ .

$f'(x) = -8x^-7$ is never $0$ and fails to exist only at $0$ , which is not in the domain of $f$ . So, $f$ has no critical numbers.

How do you find the critical numbers for f(x)= x^(-8) ln xf(x)= x^(-8) ln x to determine the maximum and minimum?