Question

The cost in dollars of producing x units of a particular brand of notebook is C(x) = x^2 – 400.

a)Find the average rate of change of C with respect to x when the production level is changed from x = 100 to x = 102. Include units in your answer.

b)Find the instantaneous rate of change of C with respect to x when x = 100. Include units in your answer.

Answer 1

really could use some help on this on !!!

Answer 2

How do you think you should approach this? what do the terms average and instantaneous mean to you?

Answer 3

well i understand the meaning of the terms im just not too sure how to go about obtaining them, for starters on problem a i know the formula but after i have the equation of the average rate of change what do i do?

Answer 4

im getting (x^2 -9604)/(x-102) for the average rate of change equation

Answer 5

\[average= \frac{ \Delta Y }{ \Delta X }\]
You need to solve for Y at each X and then use this equation

Answer 6

solve for y where ?!?

Answer 7

eabollich

Answer 8

C(x) is another way of writing Y in the equation of a line y=mx +b. Are you familiar with this equation?

Answer 9

yes

Answer 10

c(100) = 9600
c(102) = 10004
so...
(9600-10004)/(100 - 102)?

Answer 11

Yes. the negative signs cancel out.
the traditional way would be to put 10004-9600 and 102-100 but as long as you are consistent, it doesn't make a difference

Answer 12

Is this for calculus or algebra?

Answer 13

calculus ab

Answer 14

and im starting to think this is wrong

Answer 15

http://home.earthlink.net/~peggyfrisbie/images/avg%20rate%20of%20change%20back.jpg
The average rate of change is the same for calculus and algebra. The instantaneous rate is where things are easier if you are using calculus.
http://www.thebestschools.org/wp-content/uploads/2014/08/calculus2.jpg

Answer 16

Why do you think it is wrong?

Answer 17

because we didn't use an equation i was certain would be relevant

Answer 18

oh wait

Answer 19

you just proved me wrong :p

Answer 20

I changed the variables to X and Y but it is the same equation :)

Answer 21

okay and for part b do i just find the derivative at that point?

Answer 22

I assumed at first that it was an algebra class so I used X and Y, sorry for the confusion

Answer 23

I haven't taken Calculus but I assume from what I am reading that you are correct. The third example on this website gives a good example of what that looks like: http://www.millersville.edu/~bikenaga/calculus/tangent/tangent.html

Answer 24

thank's !!

Answer 25

You're welcome! Glad I could help!