Find the average rate of change of f(x)=x^3-3x from x1=-2 to x2=0.

We have been given the functionf(x)=x^3-3x
We know that the average rate of change of a function is given by
(\Delta y)/(\Delta x)= (f(x_2)-f(x_1))/(x_2-x_1)
Let us find the values of f(x_1)& f(x_2)
f(x_1)=f(-2)=(-2)^3-3(-2)=-8+6=-2
f(x_2)=f(0)=(0)^3-3(0)=0
On substituting the values of f(x_1), f(x_2), x_1 and x_2 in the above written formula for average rate of change, we get
(\Delta y)/(\Delta x)= (0-(-2))/(0-(-2))= (2)/(2)=1
Thus, the average rate of change the function f(x)=x^3-3x from x_1=-2 \text{ to} x_2=0 is 1

The average rate of change is the slope of the secant line between x_2 and x_1 . The slope of the secant line, m_s, is found in the attached image.