g(x)=-\\frac{x^{2}}{4}+7\nwhat is the average rate of change of g over the interval -2,4?
g(x)=-\\frac{x^{2}}{4}+7\nwhat is the average rate of change of g over the interval -2,4?
Answer
Explanation:
Step1: Find (g(-2))
Substitute (x = -2) into (g(x)=-\frac{x^{2}}{4}+7). [ \begin{align*} g(-2)&=-\frac{(-2)^{2}}{4}+7\ &=-\frac{4}{4}+7\ &=- 1 + 7\ &=6 \end{align*} ]
Step2: Find (g(4))
Substitute (x = 4) into (g(x)=-\frac{x^{2}}{4}+7). [ \begin{align*} g(4)&=-\frac{4^{2}}{4}+7\ &=-\frac{16}{4}+7\ &=-4 + 7\ &=3 \end{align*} ]
Step3: Calculate the average rate of change
The formula for the average rate of change of a function (y = g(x)) over the interval ([a,b]) is (\frac{g(b)-g(a)}{b - a}). Here (a=-2), (b = 4). [ \begin{align*} \frac{g(4)-g(-2)}{4-(-2)}&=\frac{3 - 6}{4 + 2}\ &=\frac{-3}{6}\ &=-\frac{1}{2} \end{align*} ]
Answer:
(-\frac{1}{2})