Question

find the average rate of change of the function f(x) = √x from x₁ = 9 to x₂ = 49.
the average rate of change is □. (simplify your answer.)

Explanation:

Step1: Find f(x1) and f(x2)

Given \(f(x)=\sqrt{x}\), when \(x_1 = 9\), \(f(x_1)=\sqrt{9}=3\); when \(x_2 = 49\), \(f(x_2)=\sqrt{49}=7\).

Step2: Use average - rate - of - change formula

The average rate of change of a function \(y = f(x)\) from \(x_1\) to \(x_2\) is \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\). Substitute \(f(x_1)=3\), \(f(x_2)=7\), \(x_1 = 9\) and \(x_2 = 49\) into the formula: \(\frac{7 - 3}{49-9}=\frac{4}{40}=\frac{1}{10}\).

Answer:

\(\frac{1}{10}\)