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Dido525
 2 years ago
Find f(4) if f(x) is defined by:
Dido525
 2 years ago
Find f(4) if f(x) is defined by:

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Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1353113577149:dw I am not sure if I can apply the fundamental theorem of Calculus here...

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0@zepdrix @TuringTest @AccessDenied

AccessDenied
 2 years ago
Best ResponseYou've already chosen the best response.2I believe that you can apply the Fundamental Theorem of Calculus here if you take the derivative of both sides with respect to x.

AccessDenied
 2 years ago
Best ResponseYou've already chosen the best response.2Equality only holds if you do to one side what you do to the other. This holds true for differentiation as well

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0so I get: 1+ln(x)=2xf(x^2)

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0I sub in 4 and solve for f(x) right?

AccessDenied
 2 years ago
Best ResponseYou've already chosen the best response.2Yes, 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)...

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0I get: dw:1353114453992:dw

AccessDenied
 2 years ago
Best ResponseYou've already chosen the best response.2Yep, 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). :)

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0Thanks a lot for helping me!

AccessDenied
 2 years ago
Best ResponseYou've already chosen the best response.2You're welcome! :)
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