Suppose that the differentiable function y = f(x) has an inverse and that the graph of ƒ passes through the point (2, 4) and has a slope of \frac13 there. Find the value of \frac{df^{-1}}{dx} at x = 4
The answer in the textbook says it's 3 but I keep getting different answers everytime I attempt the question.
My solution:
Using (2,4) and m = \frac13 I got y = \frac13x + \frac{10}3
Plugging x = 4 into the equation, I get (4, \frac{14}3)
Using (f^{-1})'(b) = \frac{1}{f'(a)} I get \frac19, which is obviously different from the textbook's answer.
Can someone help push me in the right direction?
