## Dido525 3 years ago Find f(4) if f(x) is defined by:

1. Dido525

|dw:1353113377129:dw|

2. Dido525

I got this far:

3. Dido525

|dw:1353113577149:dw| I am not sure if I can apply the fundamental theorem of Calculus here...

4. Dido525

@zepdrix @TuringTest @AccessDenied

5. 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.

6. Dido525

of both sides? why?

7. AccessDenied

Equality only holds if you do to one side what you do to the other. This holds true for differentiation as well

8. Dido525

Right...

9. Dido525

so I get: 1+ln(x)=-2xf(x^2)

10. Dido525

I sub in 4 and solve for f(x) right?

11. 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)...

12. Dido525

Right...

13. Dido525

I get: |dw:1353114453992:dw|

14. 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). :)

15. Dido525

Thanks a lot for helping me!

16. AccessDenied

You're welcome! :)