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Dido525

  • 3 years ago

Find the intervals on which the function f(x) is increasing.

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  1. Dido525
    • 3 years ago
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    |dw:1353112573724:dw|

  2. Dido525
    • 3 years ago
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    @zepdrix . I believe I would find the derivative using FTC and then antiderivative that to find f(x) right?

  3. zepdrix
    • 3 years ago
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    I think you're half right, I think you want to do the first half of what you said.

  4. zepdrix
    • 3 years ago
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    \[\large f(x)=\int\limits_{0}^{x}(1+t^2)e^{t^2}dt\] \[\huge f'(x)=(1+x^2)e^{x^2}\]

  5. zepdrix
    • 3 years ago
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    Then just find critical points to find your intervals... i think :O

  6. Dido525
    • 3 years ago
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    Yeah, but wouldn't I also need to know what f(x) is?

  7. Dido525
    • 3 years ago
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    Actually... I wouldn't right? All I need is the derivative.

  8. zepdrix
    • 3 years ago
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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).

  9. Dido525
    • 3 years ago
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    Thanks :) .

  10. Dido525
    • 3 years ago
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    Guess it's my OCD telling me to find f(x) .

  11. zepdrix
    • 3 years ago
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    hah XD

  12. zepdrix
    • 3 years ago
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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

  13. zepdrix
    • 3 years ago
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    because of the e^t^2 term :o

  14. Dido525
    • 3 years ago
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    Yeah, guess so.

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