What are the values and types of the critical points, if any, of $f (x) = x^{2} - \sqrt{x}$ $f(x) =x^2-sqrtx$ ?

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What are the values and types of the critical points, if any, of $f (x) = x^{2} - \sqrt{x}$ $f(x) =x^2-sqrtx$ ?

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Answer 1 · 2018-05-11T07:08:24

$x = 2 \sqrt[3]{2}$ $x=2root(3)(2)$ 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.)
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What are the values and types of the critical points, if any, of $f (x) = x^{2} - \sqrt{x}$ $f(x) =x^2-sqrtx$ ?

1 Answer

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What are the values and types of the critical points, if any, of f(x) =x^2-sqrtxf(x)=x2−√xf(x) =x^2-sqrtx?

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What are the values and types of the critical points, if any, of $f (x) = x^{2} - \sqrt{x}$ $f(x) =x^2-sqrtx$ ?