Find the average rate of change of ​f(x) = -3x^2 + 6 over each of the following intervals:

Question

Find the average rate of change of ​f(x) = -3x^2 + 6 over each of the following intervals:

​(a) From 1 to 3

​(b) From −2 to 0

​(c) From 3 to 6

Answer 1

To find the average rate of change, just find the slope of the line through the two end-points.

Recall: Slope = (change in y) / (change in x)

We will need two xy pairs to find the average rate of change.

(a) f(1) = -3(1)^2 + 6 = 3 ==> point (1,3)

f(3) = -3(3)^2 + 6 = -21 ==> point (3,-21)

Slope = (-21-3) / (3-1) = -24/2 = -12

(b) f(-2) = -3(-2)^2 + 6 = -6 ==> point (-2,-6)

f(0) = -3(0)^2 + 6 = 6 ==> point (0,6)

Slope = (6+6) / (0+2) = 12/2 = 6

(c) f(3) = -3(3)^2 + 6 = -21 ==> point (3,-21)

f(6) = -3(6)^2 + 6 = -102 ==> point (6,-102)

Slope = (-102+21) / (6-3) = -81/3 = -27