Suppose is differentiable on with ,

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Suppose

k

is differentiable on

[-1,5]

with

k(-1)=4

k(2)=13

, and

k(5)=7

. Let

c_1

be a number in

(-1,2)

whose tangent line slope equals the average rate of change of

k

[-1,2]

, and let

c_2

be a number in

(2,5)

whose tangent line slope equals the average rate of change of

k

[2,5]

. Which of the following must be true? (a)

k'(c_1)=k'(c_2)

(b)

k'(c_1)<k'(c_2)

(c)

k'(c_1)>k'(c_2)

(d) No relationship between

k'(c_1)

and

k'(c_2)

can be determined.