Suppose a differentiable function is defined on with tangent slopes given by ,

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Suppose a differentiable function

r

is defined on

[0,6]

with tangent slopes given by

r'(1)=1

r'(3)=2.5

, and

r'(5)=3

. The line joining the points

(0,r(0))

and

(6,r(6))

has slope

2

. Determine whether there are at least two distinct numbers

c

(0,6)

where

r'(c)=2

. Answer Yes or No and justify briefly using the provided slope information.