Question

What are the values and types of the critical points, if any, of `f(x) =x^2-sqrtx`?

Answer 1

`x=2root(3)(2)` is the minimum.

Explanation:

`f(x) =x²-sqrtx`
We search `f'(x)=0`
`f'(x)=2x+1/(2sqrt(x))`
`2x+1/(2sqrt(x))=0`
`2xsqrtx=-1/2`
`xsqrtx=-1/4`
`x³=1/16`
`x=2root(3)(2)`
Let `X=sqrtx`, we can see `f(X)=X⁴-X`, and so that `x=2root(3)(2)` as a minimum of `f(x)` (because f take the sign of his monoma of higher degree.)
\0/ here's our answer!