Posted by **Andrea** on Friday, March 28, 2014 at 7:38pm.

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!

- Calculus -
**Damon**, Friday, March 28, 2014 at 7:52pm
first

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

- Calculus -
**Damon**, Friday, March 28, 2014 at 7:57pm
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

- Calculus -
**Damon**, Friday, March 28, 2014 at 8:11pm
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

- Calculus -
**Damon**, Friday, March 28, 2014 at 8:12pm
so it is positive for x>.316

and for x <.316

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