Question

sections 1.3 - 1.4
score: 2/21 answered: 2/21
question 3
find the average rate of change of ( g(x)=-3 x^{3}-1 ) from ( x=-4 ) to ( x = 1 )

Explanation:

Step1: Recall the formula for average rate of change

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 \(g(x)=-3x^{3}-1\).

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

• For \(x=a=-4\):

\(g(-4)=-3(-4)^{3}-1=-3\times(-64)-1 = 192 - 1=191\)

• For \(x = b = 1\):

\(g(1)=-3(1)^{3}-1=-3 - 1=-4\)

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

\(\frac{g(1)-g(-4)}{1-(-4)}=\frac{-4 - 191}{1 + 4}=\frac{-195}{5}=-39\)

Answer:

\(-39\)