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Dido525

  • 2 years ago

Find f(4) if f(x) is defined by:

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  1. Dido525
    • 2 years ago
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    |dw:1353113377129:dw|

  2. Dido525
    • 2 years ago
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    I got this far:

  3. Dido525
    • 2 years ago
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    |dw:1353113577149:dw| I am not sure if I can apply the fundamental theorem of Calculus here...

  4. Dido525
    • 2 years ago
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    @zepdrix @TuringTest @AccessDenied

  5. AccessDenied
    • 2 years ago
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    I believe that you can apply the Fundamental Theorem of Calculus here if you take the derivative of both sides with respect to x.

  6. Dido525
    • 2 years ago
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    of both sides? why?

  7. AccessDenied
    • 2 years ago
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    Equality only holds if you do to one side what you do to the other. This holds true for differentiation as well

  8. Dido525
    • 2 years ago
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    Right...

  9. Dido525
    • 2 years ago
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    so I get: 1+ln(x)=-2xf(x^2)

  10. Dido525
    • 2 years ago
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    I sub in 4 and solve for f(x) right?

  11. AccessDenied
    • 2 years ago
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    Yes, that's what I am getting as well. I then note that f(x^2) = f(4) if x=2. So I would substitute in x=2 to find f(4)...

  12. Dido525
    • 2 years ago
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    Right...

  13. Dido525
    • 2 years ago
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    I get: |dw:1353114453992:dw|

  14. AccessDenied
    • 2 years ago
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    Yep, looks correct to me. If we wanted f(x) in general, we'd probably just substitute in \(x = \sqrt{u}\) so the x^2 inside f(x^2) cancels with the root, but it seems easier to just go directly from f(x^2). :)

  15. Dido525
    • 2 years ago
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    Thanks a lot for helping me!

  16. AccessDenied
    • 2 years ago
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    You're welcome! :)

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