MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions
Problem
A differentiable function g satisfies g(2)=5 and g′(2)=4. The function is strictly increasing on an open interval containing x=2.
Answer the following questions about the inverse function g−1.
(a) Determine (g−1)′(5). Show all steps that lead to your answer.
(b) Write an equation for the tangent line to the graph of g−1 at the point whose x-coordinate is 5.
(c) The tangent line found in part (b) intersects the line y=x at a certain point. Calculate the coordinates of this intersection and explain its significance in the context of the graphs of g and g−1.