Question

question 2 - 3
selected response: 1 point for answer only.
what is the average rate of change for the function ( f(x)=-2 x^{3}+x - 1 ) over the interval from ( x = 1 ) to ( x = 3 )?
-27
-25
25
27

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 1\) and \(b=3\).

Step2: Calculate \(f(1)\) and \(f(3)\)

• For \(x = 1\):

\(f(1)=-2(1)^3+(1)-1=-2 + 1-1=-2\)

• For \(x = 3\):

\(f(3)=-2(3)^3+(3)-1=-2\times27+3 - 1=-54 + 3-1=-52\)

Step3: Apply the average - rate - of - change formula

\(\frac{f(3)-f(1)}{3 - 1}=\frac{-52-(-2)}{3 - 1}=\frac{-52 + 2}{2}=\frac{-50}{2}=-25\)

Answer:

\(-25\)