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

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

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Answer 1 · 2018-06-16T12:57:51

#P_max(-0.182115825969939296277,1.087614208523047937841)#

Explanation:

We get
#f'(x)=-e^(-2x^2)(e^(x+2x^2)+4x+e^(x+2x^2)x)#
By a numerical method we get
#x_1approx -0.182115825969939296277#
and
#f''(x)=-e^(-2x^2)(4+2e^(x+2x^2)+e^(x+2x^2)x-16x^2)#
and

#f''(x_1)<0#
so we get a maximum.

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

1 Answer

Explanation:

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