t g(t) -5 6 -4 4 -3 2 -2 1 -1 -1 0 -2 1 -3 2 1 3 3 4 6 5 9 over which interval does g have an average rate…

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function (y = g(t)) over the interval ([a,b]) is given by (\frac{g(b)-g(a)}{b - a}). We want to find when (\frac{g(b)-g(a)}{b - a}=0), which implies (g(b)=g(a)).

Step2: Check each interval

• For interval (A): (-2\leq t\leq2) Here (a=-2) and (b = 2). (g(-2)=1) and (g(2)=1). Then the average rate of change is (\frac{g(2)-g(-2)}{2-(-2)}=\frac{1 - 1}{4}=0).
• For interval (B): (0\leq t\leq4) (a = 0), (b=4). (g(0)=-2) and (g(4)=6). The average rate of change is (\frac{6-(-2)}{4-0}=\frac{8}{4}=2\neq0).
• For interval (C): (1\leq t\leq3) (a = 1), (b = 3). (g(1)=-3) and (g(3)=3). The average rate of change is (\frac{3-(-3)}{3 - 1}=\frac{6}{2}=3\neq0).
• For interval (D): (-5\leq t\leq1) (a=-5), (b = 1). (g(-5)=6) and (g(1)=-3). The average rate of change is (\frac{-3 - 6}{1-(-5)}=\frac{-9}{6}=-\frac{3}{2}\neq0).

Answer:

A. (-2\leq t\leq2)