Question

"Calculate the average rate of change between x= -2 and x=4 using the equation below.

f(x) = x2 + 2x
Show ALL work in the space provided to the right.

Answer 1

To find the average rate of change for the function f(x) = x^2 + 2x from x = -2 to x = 4, calculate the function values at both points and then use the average rate of change formula: change in y over change in x. The rate of change is 4.

Step-by-step explanation:

To calculate the average rate of change of the function f(x) = x2 + 2x between x = -2 and x = 4, we need to find the values of f(x) at these points and then apply the formula for average rate of change.

First, calculate f(-2) which gives f(-2) = (-2)2 + 2(-2) = 4 - 4 = 0.

1. Next, calculate f(4) which gives f(4) = (4)2 + 2(4) = 16 + 8 = 24.
2. The change in y values (Δy) is f(4) - f(-2), so Δy = 24 - 0 = 24.
3. The change in x values (Δx) is 4 - (-2) = 4 + 2 = 6.
4. Finally, divide the change in y by the change in x to get the average rate of change: Avg rate = Δy / Δx = 24/6 = 4.

therefore, the average rate of change of the function on the interval from x = -2 to x = 4 is 4.