Question

g(x)= x^3 2x −1. what is the slope of the tangent line to the curve g^−1(x) at the point (2, 1)?

Answer 1

The slope of the inverse function of a function is the mulplicative inverse of the slope of the function.
slope of g^-1(x) = 1/slope of g(x)

g(x) = x^3 + 2x - 1
g'(x) = 3x^2 + 2
g'(2) = 3(2)^2 + 2 = 3(4) + 2 = 12 + 2 = 14
slope of g(x) at point (2, 1) = 14

Therefore, slope of g^-1(x) at point (2, 1) = 1/14