Question

What are the local extrema of `f(x)= xsqrt(x+3/x)`?

Answer 1

The function has no local extrema.

Explanation:

`f'(x) = (3x^2+3)/(2xsqrt(x+3/x))` is never `0` and is undefined only at `x=0` which is outside the domain of `f`.

Therefore, the function has no critical numbers.