# Chapter 3 - The Derivative - 3.3 Rates of Change - 3.3 Exercises: 1

6

#### Work Step by Step

y = $x^{2}$ + 2x between x = 1 and x = 3 To find the rate of change, you have to use the rate of change formula: $\frac{f(b)-f(a)}{b-a}$ In this problem, the starting point is at 1 and the end point is 3. Therefore, a = 1 and b = 3. Knowing this, you can plug these numbers back into the formula. $\frac{(3^{2}+2\times3)-(1^{2}+2\times1)}{3-1}$ = $\frac{(9+6)-(1+2)}{2}$ = $\frac{15-3}{2}$ = $\frac{12}{2}$ = 6 Therefore, the rate of change equals 6.

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