The average rate of change of a function f(x) in an interval, a < x < b is given by
[tex]\frac{f(b) - f(a)}{b - a}[/tex]
Given q(x) = (x + 3)^2
1.) The average rate of change of q(x) in the interval -6 ≤ x ≤ -4 is given by [tex] \frac{q(-4)-q(-6)}{-4-(-6)} = \frac{(-4+3)^2-(-6+3)^2}{-4+6} = \frac{1-9}{2} = \frac{-8}{2} =-4[/tex]
2.) The average rate of change of q(x) in the interval -3 ≤ x ≤ 0 is given by [tex] \frac{q(0)-q(-3)}{0-(-3)} = \frac{(0+3)^2-(-3+3)^2}{0+3} = \frac{9-0}{3} = \frac{9}{3} =3[/tex]
3.) The average rate of change of q(x) in the interval -6 ≤ x ≤ -3 is given by [tex] \frac{q(-3)-q(-6)}{-3-(-6)} = \frac{(-3+3)^2-(-6+3)^2}{-3+6} = \frac{0-9}{3} = \frac{-9}{3} =-3[/tex]
4.) The average rate of change of q(x) in the interval -3 ≤ x ≤ -2 is given by [tex] \frac{q(-2)-q(-3)}{-2-(-3)} = \frac{(-2+3)^2-(-3+3)^2}{-2+3} = \frac{1-0}{1} = \frac{1}{1} =1[/tex]
5.) The average rate of change of q(x) in the interval -4 ≤ x ≤ -3 is given by [tex] \frac{q(-3)-q(-4)}{-3-(-4)} = \frac{(-3+3)^2-(-4+3)^2}{-3+4} = \frac{0-1}{1} = \frac{-1}{1} =-1[/tex]
6.) The average rate of change of q(x) in the interval -6 ≤ x ≤ 0 is given by [tex] \frac{q(0)-q(-6)}{0-(-6)} = \frac{(0+3)^2-(-6+3)^2}{0+6} = \frac{9-9}{6} = \frac{0}{6} =0[/tex]
