   Chapter 3.10, Problem 43E

Chapter
Section
Textbook Problem

Suppose that the only information we have about a function f is that f(1) = 5 and the graph of its derivative is as shown.(a) Use a linear approximation to estimate f(0.9) and f(1.1).(b) Are your estimates in part (a) too large or too small? Explain. (a)

To determine

To estimate: The value f(0.9) and  f(0.1).

Explanation

Given:

The value f(1)=5.

Result used:

The linear approximation of the function at x=a is,f(x)f(a)+f(a)(xa).

Calculation:

Obtain the value of f(0.9).

The linearization of the function f(x) at x=0 is computed as follows,

Substitute the value a=1 in f(x)f(a)+f(a)(xa),

f(x)f(1)+f(1)(x1)

Form the given graph, it is observed that f(1)=2

(b)

To determine

To explain: Whether the estimate value in part (a) is too large or too small.

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