2. what is the average rate of change of $g(x)=x^{2}$ on the interval $3 \\leq x \\leq 9$?\n(1) 8\n(2)…

2. what is the average rate of change of $g(x)=x^{2}$ on the interval $3 \\leq x \\leq 9$?\n(1) 8\n(2) 12\n(3) 15\n(4) 18

2. what is the average rate of change of $g(x)=x^{2}$ on the interval $3 \\leq x \\leq 9$?\n(1) 8\n(2) 12\n(3) 15\n(4) 18

Answer

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function (y = g(x)) on the interval ([a,b]) is (\frac{g(b)-g(a)}{b - a}). Here, (a = 3), (b=9), and (g(x)=x^{2}).

Step2: Calculate (g(a)) and (g(b))

When (x = 3), (g(3)=3^{2}=9). When (x = 9), (g(9)=9^{2}=81).

Step3: Substitute into the formula

Substitute (g(3) = 9), (g(9)=81), (a = 3), and (b = 9) into (\frac{g(b)-g(a)}{b - a}). We get (\frac{81 - 9}{9-3}=\frac{72}{6}).

Step4: Simplify the expression

(\frac{72}{6}=12).

Answer:

(2) 12