find the average rate of change of g(x)= -5x³ + 5 from x = -4 to x = 1 enter an integer or decimal number…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = g(x)$ from $x = a$ to $x = b$ is $\frac{g(b)-g(a)}{b - a}$. Here, $a=-4$, $b = 1$, and $g(x)=-5x^{3}+5$.

Step2: Calculate $g(a)$

Substitute $x=-4$ into $g(x)$: $g(-4)=-5\times(-4)^{3}+5=-5\times(-64)+5 = 320 + 5=325$.

Step3: Calculate $g(b)$

Substitute $x = 1$ into $g(x)$: $g(1)=-5\times(1)^{3}+5=-5 + 5=0$.

Step4: Calculate the average rate of change

Substitute $g(-4)$ and $g(1)$ into the average - rate - of - change formula: $\frac{g(1)-g(-4)}{1-(-4)}=\frac{0 - 325}{1 + 4}=\frac{-325}{5}=-65$.

Answer:

$-65$