Suppose f is a one-to-one, differentiable function and its inverse function f^-1 is also differentiable. One can show, using implicit differentiation (do it!), that (f^-1)'(x) = 1 / (f'(f^-1(x))) Find (f^-1)'(-4) if f(-1) = -4 and f'(-1) = 2/7. (f^-1)'(-4) =
Added by Ngan L.
Close
Step 1
Step 1: Use the formula (f^-1)'(x) = 1 / f'(f^-1(x)) to find (f^-1)'(-4). Show more…
Show all steps
Your feedback will help us improve your experience
Vincenzo Zaccaro and 61 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
f is a one-to-one differentiable function and its inverse f^(-1) is also differentiable. Using implicit differentiation, you can show that (f^(-1))'(x) = 1 / f'(f^(-1)(x)), assuming f'(-5) = 13/7. Find (f^(-1))'(-4).
Zhumagali S.
Suppose f is a one-to-one, differentiable function and its inverse function f^-1 is also differentiable. One can show, using implicit differentiation (do it!), that (f^-1)'(x) = 1 / (f'(f^-1(x))) Find (f^-1)'(4) if f(1) = 4 and f'(1) = 13/11. (f^-1)'(4) =
Suman Saurav T.
Suppose f is a one-to-one, differentiable function and its inverse function f^{-1} is also differentiable. One can show, using implicit differentiation (do it!), that (f^{-1})'(x) = 1 / (f'(f^{-1}(x))) Find (f^{-1})'(4) if f(1) = 4 and f'(1) = 2/5. (f^{-1})'(4) =
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD