What are the local extrema of $f (x) = x \sqrt{x + \frac{3}{x}}$ $f(x)= xsqrt(x+3/x)$ ?

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Answer 1 · 2015-11-22T17:03:42

The function has no local extrema.

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

Therefore, the function has no critical numbers.

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