Find the average rate of change of fx 3x2 6 a From 1 to 3

Find the average rate of change of f(x) = -3x^2 + 6 (a) From 1 to 3 (b) From - 2 to 0 (c) From - 2 to 1 (a) From 1 to 3 (b) From - 2 to 0 (c) From - 2 to 1

Solution

Average rate of change =(f(b) - f(a))/(b-a)

a) from 1 to 3

f(x)=-3x²+6

f(1)=-3*1² + 6 = 3

f(3)=-3*3² + 6= -21

Average rate of change= (f(3)-f(1))/(3-1)= (-21-3)/(3-1)=-24/2=-12

b) from -2 to 0

f(-2)=-3*(-2)²+6=-6

f(0)=-3*(0)² + 6=6

Average rate of change= (f(0)-f(-2))/(0-(-2)) = (6-(-6))/2=6

c. from -2 to 1

f(-2)= -3*(-2)²+6 = -6

f(1) = -3*(1)²+6 = 3

average rate of change= (f(1)-f(-2))/(1-(-2))= (3-(-6))/(1-(-2))=3