# Chapter 3 - The Derivative - 3.3 Rates of Change - 3.3 Exercises - Page 158: 5

$\frac{1}{3}$

#### Work Step by Step

y = $\sqrt x$ between x = 1 and x = 4 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 1 and the end point is 4. Therefore, a = 1 and b = 4. Since you know the a and b values, you can plug them into the formula: $\frac{(\sqrt 4)-(\sqrt 1)}{4-1}$ = $\frac{2-1}{3}$ = $\frac{1}{3}$ Therefore, the average rate of change is equal to $\frac{1}{3}$

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