Dido525
Find the intervals on which the function f(x) is increasing.
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Dido525
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|dw:1353112573724:dw|
Dido525
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@zepdrix . I believe I would find the derivative using FTC and then antiderivative that to find f(x) right?
zepdrix
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I think you're half right, I think you want to do the first half of what you said.
zepdrix
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\[\large f(x)=\int\limits_{0}^{x}(1+t^2)e^{t^2}dt\]
\[\huge f'(x)=(1+x^2)e^{x^2}\]
zepdrix
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Then just find critical points to find your intervals... i think :O
Dido525
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Yeah, but wouldn't I also need to know what f(x) is?
Dido525
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Actually... I wouldn't right? All I need is the derivative.
zepdrix
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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).
Dido525
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Thanks :) .
Dido525
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Guess it's my OCD telling me to find f(x) .
zepdrix
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hah XD
zepdrix
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Hmm i could be wrong, but I don't think you can actually solve that integral using elementary methods :D heh
zepdrix
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because of the e^t^2 term :o
Dido525
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Yeah, guess so.