you might need: calculator\n$g(x)=-\\frac{x^{2}}{4}+7$\nover which interval does $g$ have a negative average…

you might need: calculator\n$g(x)=-\\frac{x^{2}}{4}+7$\nover which interval does $g$ have a negative average rate of change?\nchoose 1 answer:\na $-2,0$\nb $-4,-2$\nc $0,4$\nd $-8,-4$

you might need: calculator\n$g(x)=-\\frac{x^{2}}{4}+7$\nover which interval does $g$ have a negative average rate of change?\nchoose 1 answer:\na $-2,0$\nb $-4,-2$\nc $0,4$\nd $-8,-4$

Answer

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function (y = g(x)) over the interval ([a,b]) is given by (\frac{g(b)-g(a)}{b - a}).

Step2: Calculate the average rate of change for option A

For the interval ([-2,0]): (g(-2)=-\frac{(-2)^{2}}{4}+7=-\frac{4}{4}+7=- 1 + 7=6) (g(0)=-\frac{0^{2}}{4}+7 = 7) The average rate of change is (\frac{g(0)-g(-2)}{0-(-2)}=\frac{7 - 6}{2}=\frac{1}{2}>0)

Step3: Calculate the average rate of change for option B

For the interval ([-4,-2]): (g(-4)=-\frac{(-4)^{2}}{4}+7=-\frac{16}{4}+7=-4 + 7 = 3) (g(-2)=-\frac{(-2)^{2}}{4}+7=-1 + 7=6) The average rate of change is (\frac{g(-2)-g(-4)}{-2-(-4)}=\frac{6 - 3}{2}=\frac{3}{2}>0)

Step4: Calculate the average rate of change for option C

For the interval ([0,4]): (g(0)=-\frac{0^{2}}{4}+7=7) (g(4)=-\frac{4^{2}}{4}+7=-4 + 7=3) The average rate of change is (\frac{g(4)-g(0)}{4 - 0}=\frac{3-7}{4}=\frac{-4}{4}=-1<0)

Step5: Calculate the average rate of change for option D

For the interval ([-8,-4]): (g(-8)=-\frac{(-8)^{2}}{4}+7=-\frac{64}{4}+7=-16 + 7=-9) (g(-4)=-\frac{(-4)^{2}}{4}+7=-4 + 7=3) The average rate of change is (\frac{g(-4)-g(-8)}{-4-(-8)}=\frac{3-(-9)}{4}=\frac{12}{4}=3>0)

Answer:

C. ([0,4])