anonymous
  • anonymous
Find the intervals on which the function f(x) is increasing.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
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anonymous
  • anonymous
@zepdrix . I believe I would find the derivative using FTC and then antiderivative that to find f(x) right?
zepdrix
  • zepdrix
I think you're half right, I think you want to do the first half of what you said.

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zepdrix
  • zepdrix
\[\large f(x)=\int\limits_{0}^{x}(1+t^2)e^{t^2}dt\] \[\huge f'(x)=(1+x^2)e^{x^2}\]
zepdrix
  • zepdrix
Then just find critical points to find your intervals... i think :O
anonymous
  • anonymous
Yeah, but wouldn't I also need to know what f(x) is?
anonymous
  • anonymous
Actually... I wouldn't right? All I need is the derivative.
zepdrix
  • zepdrix
Yah I don't think they want us to SOLVE for f(x). They've given us f(x), it just looks a little funny. We simply want intervals of increasing/decreasing. So we only need to deal with f'(x).
anonymous
  • anonymous
Thanks :) .
anonymous
  • anonymous
Guess it's my OCD telling me to find f(x) .
zepdrix
  • zepdrix
hah XD
zepdrix
  • zepdrix
Hmm i could be wrong, but I don't think you can actually solve that integral using elementary methods :D heh
zepdrix
  • zepdrix
because of the e^t^2 term :o
anonymous
  • anonymous
Yeah, guess so.

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