Question

Find the average rate of change of g(x)= -4x^3+1 from x= -4 to x = 1

Answer 1

`Rate = -52`

Explanation:

Given

`g(x) = -4x^3 + 1`

x = -4 to x = 1

Required

Determine the average rate of change

This is calculated using:

`Rate = (g(b) - g(a))/(b - a)`

Where

`a = x = -4`

`b = x = 1`

Calculating g(b):

g(b) = g(1)

If
`g(x) = -4x^3 + 1`, then

`g(1) = -4(1)^3 + 1`

`g(1) = -4*1 + 1`

`g(1) = -4 + 1`

`g(1) = -3`

Calculating g(a):

g(a) = g(-4)

If
`g(x) = -4x^3 + 1`, then

`g(-4) = -4(-4)^3 + 1`

`g(-4) = -4*-64 + 1`

`g(-4) = 256 + 1`

`g(-4) = 257`

So, the formula:

`Rate = (g(b) - g(a))/(b - a)`

becomes

`Rate = (g(1) - g(-4))/(1 - (-4))`

`Rate = (g(1) - g(-4))/(1+4)`

`Rate = (g(1) - g(-4))/(5)`

`Rate = (-3 - 257)/(5)`

`Rate = (-260)/(5)`

`Rate = -52`