Asked by Jan

Find the points of inflection.

f(x) = e^(-x^2)

I need to know step by step how you would get the points of inflection.

Answers

Answered by Reiny
differentiate using the product rule, then differentiate again.
set that result equal to zero and solve for x

that x value is the x value of the point of inflection.
sub it back into the original to get the corresponding y value.
Answered by Reiny
sorry,
there is no product rule here in the 1st derivative, but there will be one in the 2nd
Answered by Jan
I solved it for the second derivative. So I would use that to find the points?
Answered by Jan
Is the inflection point -2?
Answered by Mgraph
((e^(-x^2))'=-2xe^(-x^2)
((e^(-x^2))''=-2e^(-x^2)+4x^2e^(-x^2)=
2e^(-x^2)(2x^2-1)=0
Two points: (sqrt(1/2),e^(-1/2))
(-sqrt(1/2),e^(-1/2))
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