When g is the inverse of f(x)= x^3+5x-4 find the value of g'(14)?

Question

hint f(2)=14

Answer 1

g is inverse of f

so g'(f(x)) = 1/f'(x)
g'(14) = 1/f'(2)

now f(x) = x^3+5x-4
f'(x) = 3x^2+5
f'(2) = 17

so g'(14) = 1/f'(2) = 1/17