A differentiable function is strictly increasing on its domain
MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions
Problem
A differentiable function f is strictly increasing on its domain. Selected values of f and its derivative are shown in the table.
x
−2
−1
0
1
2
4
f(x)
−5
−2
0
3
4
6
f′(x)
0.4
0.6
1.0
1.8
2.1
2.4
(a) Determine (f−1)′(4). Show all work and justify your answer using only the information provided in the table.
(b) Write the equation of the line tangent to y=f−1(x) at x=4. Express your answer in point–slope form, and include an explanation of how you obtained both the point of tangency and the slope.