Question

Use the following graph of the function f(x) = x3 − 3x2 − x + 3 to answer this question: graph of x cubed minus 3 x squared minus x plus 3 What is the average rate of change from x = −1 to x = 2?

Answer 1

The average rate of change is also known as the slope. If we are looking to find the average rate of change between x = -1 and x = 2, in order to find the slope between those 2 x values, we need the y's that go along with them. Fill in -1 for x in the function and solve for y: $(-1)^3-3(-1)^2-(-1)+3=0$. That means that the coordinate is (-1, 0). Fill in 2 for x in the function and solve for y: $(2)^3-3(2)^2-(2)+3=-3$. The coordinate there is (2, -3). Now we can set up the slope formula to find the average rate of change between those 2 points: $\frac{-3-0}{2-(-1)}=\frac{-3}{3}=-1$. Therefore, the average rate of change between x = -1 and x = 2 is -1