Question

f(x) = 0.25x^3 + x - 1. What is the value of the derivative of the inverse when x=3?

Answer 1

f(2) = 3
if g(x) = f^{^-1}(x) then if f(a) = b, g'(b) = 1/f'(a)
f'(x) = 3/4 x^2 + 1
so f'(2) = 4
Thus, (f^{^-1})'(3) = 1/f'(2) = 1/4

This might be helpful:

calcworkshop.com/derivatives/derivative-of-inverse-function/