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.
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.
5 answers
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
I solved it for the second derivative. So I would use that to find the points?
Is the inflection point -2?
((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))
3 answers