Question

Find the average rate of change for the function

Answer 1

average rate of change on [-1,3] = 11

Explanation:

avg rate of change =
`(f(b)-f(a))/(b-a)`

`(f(3)-f(-1))/(3-(-1))`

1. find your y-values.

we are given the x values from the interval [-1,3]. Plug each into the equation to get the y-value of the coordinates.

`f(-1)=4(-1)^2+3(-1)-4\\f(-1)=4(1)-3-4\\f(-1)=-3\\`

coordinate: (–1,3)

`f(3)=4(3)^2+3(3)-4\\f(3)=4(9)+9-4\\f(3)=36+9-4\\f(3)=41`

coordinate: (3, 41)

2. plug into the slope formula

`m=(y_(2) -y_(1) )/(x_(2) -x_(1) ) \\m=(41-(-3))/(3-(-1)) \\m=(41+3)/(4) \\m=(44)/(4) \\m=11`