find the average rate of change

Question

How to find the average rate of change of f(x)=3x^2+4

A.from 0 to2

B. from -2 to 0

C.from 0 to 3

Answer 1

Given function f(x) = 3x^2+4

A) a = 0, b = 2

f(0) = 3(0)^2+4 = 4

f(2) = 3(2)^2+4 = 12+4 = 16

Average rate ofchange = (f(b)-f(a))/(b-a)

= (16-4)/(2-0)

= 12/2

= 6

B) a = -2, b = 0

f(a) = 3(-2)^2+4 = 3(4)+4 = 12+4 = 16

f(b) = 3(0)^2+4 = 4

Average rate ofchange = (f(b)-f(a))/(b-a)

= (16-4)/(-2-0)

= 12/-2

= -6

C) a = 0,b = 3

f(a) = 4

f(b) = 3(3)^2+4 = 3*9+4 = 27+4 = 31

Average rate ofchange = (f(b)-f(a))/(b-a)

= (31-4)/(3-0)

= 27/3

= 9