question 2 - 3\nselected response: 1 point for answer only.\nwhat is the average rate of change for the…

question 2 - 3\nselected response: 1 point for answer only.\nwhat 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 )?\n-27\n-25\n25\n27

question 2 - 3\nselected response: 1 point for answer only.\nwhat 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 )?\n-27\n-25\n25\n27

Answer

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)