What are the critical points of $g (x) = e^{x^{2}} (x - 10)$ $g(x)=e^(x^2)(x-10)$ ?

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Answer 1 · 2017-08-21T01:26:21

$x = \frac{2 \pm \sqrt{23}}{2}$ $x= (2+-sqrt23)/2$

Domain of $g$ $g$ is $RR$

$g'(x) = 2xe^(x^2)(x-10) + e^(x^2)$

$= e^(x^2)(2x^2-10x+1)$

$g'(x)$ is never undefined and $g'(x) = 0$ at

$2x^2-10x+1=0$

$x = (-(-10)+-sqrt((-10)^2-4(2)(1)))/(2(2))$

$= (10+-sqrt92)/4 = (10+-2sqrt23)/4 = (2+-sqrt23)/2$

What are the critical points of g(x)=e^(x^2)(x-10)g(x)=ex2(x−10)g(x)=e^(x^2)(x-10)?