Question

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

Answer 1

`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`