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

Mar 28, 2015

$f \left(x\right) y = x + 2 {x}^{-} 1 = x + \frac{2}{x}$

$f ' \left(x\right) = y ' = 1 - \frac{2}{x} ^ 2 = \frac{{x}^{2} - 2}{x} ^ 2$

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

$f ' \left(x\right) = 0$ when ${x}^{2} - 2 = 0$, so $x = \pm \sqrt{2}$ which are both in the domain of $f$.

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

The critical points for $f \left(x\right) y = x + 2 {x}^{-} 1 = x + \frac{2}{x}$ are $\pm \sqrt{2}$