What are the critical values of $f (x) = \frac{x}{e^{x + x^{2}}} - x^{2}$ $f(x)=x/e^(x+x^2)-x^2$ ?

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What are the critical values of $f (x) = \frac{x}{e^{x + x^{2}}} - x^{2}$ $f(x)=x/e^(x+x^2)-x^2$ ?

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Answer 1 · 2018-06-01T16:40:42

$x \approx 0.2397184192$ $xapprox 0.2397184192$

Explanation:

Writing $f (x)$ $f(x)$ in the following form
$f (x) = x \cdot e^{- x - x^{2}} - x^{2}$ $f(x)=x*e^(-x-x^2)-x^2$
so
$f'(x)=e^(-x-x^2)+x*e^(-x-x^2)(-2x-1)-2x$
this equation can only be solved by a numerical method:
$xapprox 0.2397184192$

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What are the critical values of $f (x) = \frac{x}{e^{x + x^{2}}} - x^{2}$ $f(x)=x/e^(x+x^2)-x^2$ ?

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What are the critical values of f(x)=x/e^(x+x^2)-x^2f(x)=xex+x2−x2f(x)=x/e^(x+x^2)-x^2?

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What are the critical values of $f (x) = \frac{x}{e^{x + x^{2}}} - x^{2}$ $f(x)=x/e^(x+x^2)-x^2$ ?