The revenue (in thousands of dollars) from producing x units of an item is modeled by r(x) = 12x -0.005x^2.
find the average rate of change in revenue as x changes from 1001 to 1008.
the average rate of change in revenue is dollars per unit.
(do not round until the final answer. then round to the nearest integer as needed.)
i just need to know how to solve this problem, i know the answer. you!

2

Step-by-step explanation:

Average rate of change is just the slope.

You want to find the slope of the line that goes through x=1001 and x=1008 while on R(x)=12x-0.005x^2.

So y=R(x)... R(x) will give your corresponding y values for the x's mentioned.

Just plug them in.

R(1001)=12(1001)-0.005(1001)^2=7001.995

R(1008)=12(1008)-0.005(1008)^2=7015.68

So now the question just becomes find the slope of the line that goes through

(1001,7001.995) and (1008,7015.68).

To find the slope of a line given two points: I just lined the points up and subtract vertically.  Afterwards I put the second number on top of the first number.

So let's do that!

(1008 ,  7015.68)

-(1001,    7001.995)

      7       13.685

So the slope also known as the average rate of change here is 13.685/7.

Putting 13.685 divided by 7 into my calculator returns the value 1.955.

This rounded to the nearest integer is 2.

you first to choose the points and then move from then as the slope you have