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

Limits, differentiation, related rates, integration, trig integrals, etc.

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

Postby jaybird0827 on Wed Jul 01, 2009 12:02 am

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?
User avatar
jaybird0827
 
Posts: 24
Joined: Tue May 26, 2009 6:31 pm
Location: NC

Sponsor

Sponsor
 

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

Postby Martingale on Wed Jul 01, 2009 3:58 am

jaybird0827 wrote: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?


User avatar
Martingale
 
Posts: 363
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA

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

Postby jaybird0827 on Wed Jul 01, 2009 9:08 pm

Martingale wrote:


I did wonder if I'd messed up on the 2nd derivative. Thanks, Martingale! :clap:
User avatar
jaybird0827
 
Posts: 24
Joined: Tue May 26, 2009 6:31 pm
Location: NC


Return to Calculus