Suppose g is the inverse function of f and f(4) = 5, f(5) = 2, f'(4) = -3/4 , and f'(5) = 2/3. Find g'(5).

Question

Calculus 2 homework problem and I don't even know where to begin. Thank you for any help.

Answer 1

The inverse rule for derivatives says that if f and g are inverses then g'(x) = 1/f '(g(x))

So g'(5) = 1/f '(g(5))

Because f(4) = 5 then we know that g(5) = 4 (because they are inverse functions)

So g'(5) = 1/f '(4) = 1/(-3/4) = -4/3