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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.

44. f ( x ) = 1 2 x + 3

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

Explanation

Given:

The function is f(x)=12x+3 (1)

Calculation:

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

f(x)=12x+3f(a+h)=12(a+h)+3[a(b+c)=ab+ac]=12a12h+3

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

f(x)=12x+3f(a)=12a+3

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

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