   Chapter 3.2, Problem 25E

Chapter
Section
Textbook Problem

# If f ( 1 ) = 10 and f ′ ( x ) ≥ 2 for 1 ≤ x ≤ 4 , how small can f ( 4 ) possibly be?

To determine

To find:

Smallest possible value of f(4)

Explanation

1) Concept:

Using the Mean Value Theorem simplify

2) Theorem:

Mean Value Theorem: If f is the function that satisfies following hypotheses:

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:

f1=10 and f'(x)2 for 1x4

4) Calculation:

f is differentiable

f is continuous

By applying Mean value theorem on [1,4]

There exists number c such that f4-f

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