Answer
$(f^{-1})'(5)=\frac{3}{2}$
Work Step by Step
Since $f(4)=5$, this implies $f^{-1}(5)=4$ and so, by theorem 7, $(f^{-1})'(5)=\frac{1}{f'(f^{-1}(5))}=\frac{1}{f'(4)}=\frac{3}{2}.$
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 6 - Inverse Functions - 6.1 Inverse Functions - 6.1 Exercises - Page 407: 43
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