Question

At what interval is e^(-5x^2) concave up?

I know the second derivative is
100x^2*e^-5x^2-10*e^-5x^2

but I just can not figure this one out.
Thank you for your help!

Answer 1

first
http://www.wolframalpha.com/input/?i=plot++e^%28-5x^2%29

Answer 2

first
http://www.wolframalpha.com/input/?i=plot++e^%28-5x^2%29

Then this for second derivative and graph

https://www.wolframalpha.com/input/?i=second+derivative+of+e^%28-5x^2%29

Answer 3

Note that you did the second derivative correctly. It is easier to write it their way y" = 10e^(-5x^2)(10x^2-1)
It is zero at x = +/- .316

Answer 4

so it is positive for x>.316
and for x <.316