## anonymous one year ago 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.

1. anonymous

really could use some help on this on !!!

2. anonymous

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

3. anonymous

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?

4. anonymous

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

5. anonymous

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

6. anonymous

solve for y where ?!?

7. anonymous

eabollich

8. anonymous

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

9. anonymous

yes

10. anonymous

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

11. anonymous

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

12. anonymous

Is this for calculus or algebra?

13. anonymous

calculus ab

14. anonymous

and im starting to think this is wrong

15. anonymous

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

16. anonymous

Why do you think it is wrong?

17. anonymous

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

18. anonymous

oh wait

19. anonymous

you just proved me wrong :p

20. anonymous

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

21. anonymous

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

22. anonymous

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

23. anonymous

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

24. anonymous

thank's !!

25. anonymous

You're welcome! Glad I could help!