Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 0 - Before Calculus - 0.2 New Functions From Old - Exercises Set 0.2: 53

Answer

6x + 3h 3(w + x)

Work Step by Step

f(x) = 3x² - 5 f(x + h) = 3(x + h)² - 5 = 3x² + 6hx + 3h² - 5 [f(x + h) - f(x)]/h = [(3x² + 6hx + 3h² - 5) - (3x² - 5)]/h = = (6hx + 3h²)/h = 6x + 3h f(w) = 3w² - 5 [f(w) - f(x)]/(w - x) = [(3w² - 5) - (3x² - 5)]/(w - x) = = (3w² - 3x²)/(w - x) = 3(w + x)(w - x)/(w - x) = 3(w + x)
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