Problem 60 - College Algebra

Question

Find the average rate of change of the function from \(x_{1}\) to \(x_{2}.\) $$f(x)=\sqrt{x} \text { from } x_{1}=9 \text { to } x_{2}=16$$

Step-by-Step Solution

Answer

The average rate of change for the function \(f(x) = \sqrt{x}\) from \(x_1 = 9\) to \(x_2 = 16\) is \(1/7\).

Step 1: Analyzing the given function

The given function for this problem is \(f(x) = \sqrt{x}\). It's also given that \(x_1 = 9\) and \(x_2 = 16\).

Step 2: Evaluate the function at the given \(x_1\) and \(x_2\)

First, evaluate the function at \(x_1 = 9\) and \(x_2 = 16\). Thus, \(f(x_1) = f(9) = \sqrt{9} = 3\) and \(f(x_2) = f(16) = \sqrt{16} = 4\).

Step 3: Compute average rate of change

Now, using the formula for the average rate of change which is \((f(x_2) - f(x_1))/(x_2 - x_1)\), it can be calculated as \((4 - 3)/(16 - 9) = 1/7 \).