Questions: Find the average rate of change of the function (f(x)=5x) from (x1=0) to (x2=4). The average rate of change is (square) (Simplify your answer.)

Transcript text: Find the average rate of change of the function $f(x)=5 x$ from $x_{1}=0$ to $x_{2}=4$. The average rate of change is $\square$ (Simplify your answer.)

Solution

Solution Steps

Step 1: Define the Function and Interval

We are given the function $ f(x) = 5x $ and the interval from $ x_1 = 0 $ to $ x_2 = 4 $.

Step 2: Calculate Function Values at Endpoints

Evaluate the function at the endpoints of the interval: \[ f(x_1) = f(0) = 5 \cdot 0 = 0 \] \[ f(x_2) = f(4) = 5 \cdot 4 = 20 \]

Step 3: Calculate the Average Rate of Change

The average rate of change of the function over the interval $[x_1, x_2]$ is given by: \[ \text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} \] Substitute the values we calculated: \[ \text{Average Rate of Change} = \frac{20 - 0}{4 - 0} = \frac{20}{4} = 5 \]