   Chapter 3.2, Problem 26E

Chapter
Section
Textbook Problem

# Suppose that 3 ≤ f ′ ( x ) ≤ 5 for all values of x. Show that 18 ≤ f ( 8 ) − f ( 2 ) ≤ 30 .

To determine

To show:

18f8-f(2)30

Explanation

1) Concept:

Using the Mean Value Theorem simplify

2) Theorem:

Mean value theorem: If f be thefunction that satisfies the following hypothesis:

1) f is continuous on [a,b]

2) f is differentiable on (a,b)

Then, there is number c  in (a,b) such that f'c=fb-f(a)b-a

3) Given:

3f'(x)5(1)

4) Calculation:

f is differentiable

f  is continuous

By Mean value theorem on [2,8]

There exists number c

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