Inverse Question: (Help before final exam)

Dec 2009
96
1
I have my calc final today and forget how to do problems like this:

Let f(x) = 2x^2 (x is greater than or equal to 0) Find df^-1/dx at x=3

I know there is a formula 1/(f' (f^-1(b)) I am having trouble figuring out how to compute this can someone please show me! Thanks!
 
Jan 2010
564
242
Kuwait
You can use this formula, or simply, you can find the inverse function itself and evaluate its derivative when x=3 ..
We have \(\displaystyle f(x)=2x^2\) with \(\displaystyle x\geq 0\), so its a one-to-one function since its an increasing function ..
Clearly, \(\displaystyle f^{-1}(x)=\sqrt{\frac{x}{2}}=\frac{1}{\sqrt{2}} \cdot \sqrt{x}\) ..

Differentiate it, and evaluate its derivative at x=3 ..