Find the average rate of change of fx x2 2 a From 1 to 1 b F

Find the average rate of change of f(x) x2 +2: (a) From -1 to 1 (b) From -2 to 0 (c) From 3 to 6

Solution

f(x)=x²+2

average rate of change of f(x) in [a,b] = [f(b)-f(a)]/(b-a)

a)from -1 to 1

average rate of change=[(1²+2)-((-1)²+2)]/[1-(-1)]

average rate of change=[3-3]/[2]

average rate of change=0

b)from -2 to 0

average rate of change=[(0²+2)-((-2)²+2)]/[0-(-2)]

average rate of change=[2-6]/[2]

average rate of change=-2

c)from 3 to 6

average rate of change=[(6²+2)-(3²+2)]/[6-3]

average rate of change=[38-11]/[3]

average rate of change=9