find the average rate of change of $g(x)=-4x^{2}+5$ over the interval $-4,-2$. write your answer as an…

find the average rate of change of $g(x)=-4x^{2}+5$ over the interval $-4,-2$. write your answer as an integer, fraction, or decimal rounded to the nearest tenth. simplify any fractions.

find the average rate of change of $g(x)=-4x^{2}+5$ over the interval $-4,-2$. write your answer as an integer, fraction, or decimal rounded to the nearest tenth. simplify any fractions.

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)) over the interval ([a,b]) is (\frac{g(b)-g(a)}{b - a}). Here (a=-4), (b = - 2), and (g(x)=-4x^{2}+5).

Step2: Calculate (g(-4)) and (g(-2))

  • For (x=-4): (g(-4)=-4\times(-4)^{2}+5=-4\times16 + 5=-64 + 5=-59)
  • For (x=-2): (g(-2)=-4\times(-2)^{2}+5=-4\times4+5=-16 + 5=-11)

Step3: Substitute into the average - rate - of - change formula

(\frac{g(-2)-g(-4)}{-2-(-4)}=\frac{-11-(-59)}{-2 + 4}=\frac{-11 + 59}{2}=\frac{48}{2})

Answer:

(24)