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For what values of x is the curve y=e^(-x^2) ...?

Posted: Wed Jul 01, 2009 12:02 am
by jaybird0827
Problem: For what values of is the curve concave downward?

OK, so this calls for a 2nd derivative test. So this is what I did:

. That was easy. But now we have a product.



. Now, if I'm looking for concave downward, I want the value of the expression to be ,

. We know ; then we must be really looking for

That's how far I got with it. The answer is supposed to be the interval .
Did I botch something somewhere?

Re: For what values of x is the curve y=e^(-x^2) ...?

Posted: Wed Jul 01, 2009 3:58 am
by Martingale
Problem: For what values of is the curve concave downward?

OK, so this calls for a 2nd derivative test. So this is what I did:

. That was easy. But now we have a product.



. Now, if I'm looking for concave downward, I want the value of the expression to be ,

. We know ; then we must be really looking for

That's how far I got with it. The answer is supposed to be the interval .
Did I botch something somewhere?

Re: For what values of x is the curve y=e^(-x^2) ...?

Posted: Wed Jul 01, 2009 9:08 pm
by jaybird0827

I did wonder if I'd messed up on the 2nd derivative. Thanks, Martingale! :clap: