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Dido525
 3 years ago
Find the intervals on which the function f(x) is increasing.
Dido525
 3 years ago
Find the intervals on which the function f(x) is increasing.

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Dido525
 3 years ago
Best ResponseYou've already chosen the best response.0@zepdrix . I believe I would find the derivative using FTC and then antiderivative that to find f(x) right?

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1I think you're half right, I think you want to do the first half of what you said.

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1\[\large f(x)=\int\limits_{0}^{x}(1+t^2)e^{t^2}dt\] \[\huge f'(x)=(1+x^2)e^{x^2}\]

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1Then just find critical points to find your intervals... i think :O

Dido525
 3 years ago
Best ResponseYou've already chosen the best response.0Yeah, but wouldn't I also need to know what f(x) is?

Dido525
 3 years ago
Best ResponseYou've already chosen the best response.0Actually... I wouldn't right? All I need is the derivative.

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1Yah 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
 3 years ago
Best ResponseYou've already chosen the best response.0Guess it's my OCD telling me to find f(x) .

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1Hmm i could be wrong, but I don't think you can actually solve that integral using elementary methods :D heh

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1because of the e^t^2 term :o
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