Mathematics

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)

r'(B) > r'(A) > r'(C)

r'(A) > r'(C) > r'(B)

r'(A) > r'(B) > r'(C)