How do you find the critical points for $y=x+2x^-1$ ?

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Answer 1 · 2015-03-28T01:02:52

$f(x) y=x+2x^-1=x+2/x$

$f'(x)=y'=1-2/x^2=(x^2-2)/x^2$

Critical points are points in the domain at which $f'(x)=0$ or $f'(x)$ does not exist

$f'(x)=0$ when $x^2-2=0$ , so $x= +- sqrt2$ which are both in the domain of $f$ .

$f'(x)$ does not exist at $x=0$ which is not in the domain of $f$ , hence is not a critical point.

The critical points for $f(x) y=x+2x^-1=x+2/x$ are $+- sqrt2$

How do you find the critical points for y=x+2x^-1y=x+2x^-1?