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

1. Dido525

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2. Dido525

@zepdrix . I believe I would find the derivative using FTC and then antiderivative that to find f(x) right?

3. zepdrix

I think you're half right, I think you want to do the first half of what you said.

4. zepdrix

$\large f(x)=\int\limits_{0}^{x}(1+t^2)e^{t^2}dt$ $\huge f'(x)=(1+x^2)e^{x^2}$

5. zepdrix

Then just find critical points to find your intervals... i think :O

6. Dido525

Yeah, but wouldn't I also need to know what f(x) is?

7. Dido525

Actually... I wouldn't right? All I need is the derivative.

8. 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).

9. Dido525

Thanks :) .

10. Dido525

Guess it's my OCD telling me to find f(x) .

11. zepdrix

hah XD

12. zepdrix

Hmm i could be wrong, but I don't think you can actually solve that integral using elementary methods :D heh

13. zepdrix

because of the e^t^2 term :o

14. Dido525

Yeah, guess so.