Question

What is the average rate of change of Ax), represented by the table of values, over the interval [-3,2]? X AX) -5 -150 -3 -36 -1 -2 0 0 1 0 2 4 A -40 B. -8 C. 8 D. 32

Answer 1

We can calculate the average rate of change over an interval taking the variation of f(x) in the interval (between the last and first point) and dividing it by the difference between the last and first value of x.

For example, for an interval [a,b], the average rate of change is:

`r=(f(b)-f(a))/(b-a)`

In this case, the interval is [-3,2], so we can write:

`r=(f(2)-f(-3))/(2-(-3))=(4-(-36))/(2+3)=(40)/(5)=8`

Answer: the average rate of change of f(x) in the interval [-3,2] is r=8.