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# Exact Value of a Derivative Problem: You have been calculating approximate values of ISBN: 9781559536547 285

## Solution for problem c1 Chapter 1-6

Calculus: Concepts and Applications | 2nd Edition

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Problem c1

Exact Value of a Derivative Problem: You have been calculating approximate values of derivatives by finding the change in y for a given change in x, then dividing. In this problem you will apply the concept of limit to the concept of derivative to find the exact value of a derivative. Let y = f(x) = x2 7x + 11. a. Find f(3). b. Suppose that x is slightly different from 3. Find an expression in terms of x for the amount by which y changes, f(x) f(3). c. Divide the answer to part b by x 3 to get an expression for the approximate rate of change of y. Simplify. d. Find the limit of the fraction in part c as x approaches 3. The answer is the exact rate of change at x = 3.

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##### ISBN: 9781559536547

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