Let be differentiable on with and

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Let

h

be differentiable on

[2,6]

with

h(2)=5

and

h(6)=21

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

c

(2,6)

for which

h'(c)=4

. (b) For every

x

(2,6)

h'(x)=4

. (c) There exists a

c

(2,6)

for which

h'(c)=2

. (d)

h'(x)\le 4

for all

x

(2,6)