Question
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.
f(x) = e^(-x^2)
I need to know step by step how you would get the points of inflection.
Answers
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.
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.
Reiny
sorry,
there is no product rule here in the 1st derivative, but there will be one in the 2nd
there is no product rule here in the 1st derivative, but there will be one in the 2nd
Jan
I solved it for the second derivative. So I would use that to find the points?
Jan
Is the inflection point -2?
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))
((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))