anonymous
  • anonymous
Find f(4) if f(x) is defined by:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
|dw:1353113377129:dw|
anonymous
  • anonymous
I got this far:
anonymous
  • anonymous
|dw:1353113577149:dw| I am not sure if I can apply the fundamental theorem of Calculus here...

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anonymous
  • anonymous
@zepdrix @TuringTest @AccessDenied
AccessDenied
  • AccessDenied
I believe that you can apply the Fundamental Theorem of Calculus here if you take the derivative of both sides with respect to x.
anonymous
  • anonymous
of both sides? why?
AccessDenied
  • AccessDenied
Equality only holds if you do to one side what you do to the other. This holds true for differentiation as well
anonymous
  • anonymous
Right...
anonymous
  • anonymous
so I get: 1+ln(x)=-2xf(x^2)
anonymous
  • anonymous
I sub in 4 and solve for f(x) right?
AccessDenied
  • AccessDenied
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)...
anonymous
  • anonymous
Right...
anonymous
  • anonymous
I get: |dw:1353114453992:dw|
AccessDenied
  • AccessDenied
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). :)
anonymous
  • anonymous
Thanks a lot for helping me!
AccessDenied
  • AccessDenied
You're welcome! :)

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