At three distinct points and on the graph of a differentiable function
MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
At three distinct points A,B, and C on the graph of a differentiable function r, the tangent lines have the following appearances:
• At A, the line rises 2 units for every 1 unit it runs to the right.
• At B, the line is horizontal.
• At C, the line falls 1 unit for every 3 units it runs to the right.
Which of the following lists the three derivative values r′(A),r′(B),r′(C) from greatest to least?
(a) r′(C)>r′(A)>r′(B)
(b) r′(B)>r′(A)>r′(C)
(c) r′(A)>r′(C)>r′(B)
(d) r′(A)>r′(B)>r′(C)