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Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640
Textbook Problem

In Exercises 43-46, find f(a + h) – f(a) for each function. Simplify yoiir answer.

46. f(x) = x2 − 2x + 1

To determine
The value of f(a+h)f(a) for the given function.

Explanation

Given:

The function is f(x)=x22x+1 (1)

Calculation:

Substitute (a+h) for x in equation (1) to evaluate the expression in terms of (a+h) .

f(x)=x22x+1f(a+h)=(a+h)22(a+h)+1=(a2+2ah+h2)2a2h+1[(a+b)2=a2+2ab+b2]=a2+2ah+h22a2h+1

Substitute a for x in equation (1) to evaluate the expression in terms of a.

f(x)=x22x+1f(a)=a22a+1

Subtract f(a) from f(a+h) to evaluate the final expression

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