## Dido525 Group Title Find f(4) if f(x) is defined by: one year ago one year ago

1. Dido525 Group Title

|dw:1353113377129:dw|

2. Dido525 Group Title

I got this far:

3. Dido525 Group Title

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

4. Dido525 Group Title

@zepdrix @TuringTest @AccessDenied

5. AccessDenied Group Title

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 Group Title

of both sides? why?

7. AccessDenied Group Title

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

8. Dido525 Group Title

Right...

9. Dido525 Group Title

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

10. Dido525 Group Title

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

11. AccessDenied Group Title

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 Group Title

Right...

13. Dido525 Group Title

I get: |dw:1353114453992:dw|

14. AccessDenied Group Title

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 Group Title

Thanks a lot for helping me!

16. AccessDenied Group Title

You're welcome! :)