Math Problem Statement
let f(x) be a differentiable function and f^(-1) (x) be its inverse function. let g(x) = 2f(x) + (f^-1(x))^2. it is given that f(1) =1 and f'(1) = 1/2. find the value of g'(1)
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Differentiation
Inverse Functions
Chain Rule
Derivative of Inverse Function
Formulas
g(x) = 2f(x) + (f^{-1}(x))^2
g'(x) = 2f'(x) + 2f^{-1}(x) * (1 / f'(f^{-1}(x)))
(f^{-1})'(x) = 1 / f'(f^{-1}(x))
Theorems
Inverse Function Theorem
Chain Rule
Suitable Grade Level
University (Calculus I/II level)