- #1
XJellieBX
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Homework Statement
Set f(x)=[tex]\int^{2x}_{1}[/tex][tex]\sqrt{16 + t^{4}}[/tex]dt.
A. Show that f has an inverse.
B. Find ([tex]f^{-1}[/tex])'(0).
Homework Equations
([tex]f^{-1}[/tex])'(x)=1/(f'([tex]f^{-1}[/tex](x)))
The Attempt at a Solution
A. f'(x)=[tex]\sqrt{16 + t^{4}}[/tex] >0, so f is always increasing, hence one-to-one. By definition of inverse functions, f would have an inverse.
B. ([tex]f^{-1}[/tex])'(0)=1/(f'([tex]f^{-1}[/tex](0)))
I'm not sure where to go from here for part B. Help?