Chapter 0 - Before Calculus - 0.2 New Functions From Old - Exercises Set 0.2 - Page 26: 54

2x + h + 6 w + x + 6

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