anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
really could use some help on this on !!!
anonymous
  • anonymous
How do you think you should approach this? what do the terms average and instantaneous mean to you?
anonymous
  • 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?

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anonymous
  • anonymous
im getting (x^2 -9604)/(x-102) for the average rate of change equation
anonymous
  • anonymous
\[average= \frac{ \Delta Y }{ \Delta X }\] You need to solve for Y at each X and then use this equation
anonymous
  • anonymous
solve for y where ?!?
anonymous
  • anonymous
eabollich
anonymous
  • anonymous
C(x) is another way of writing Y in the equation of a line y=mx +b. Are you familiar with this equation?
anonymous
  • anonymous
yes
anonymous
  • anonymous
c(100) = 9600 c(102) = 10004 so... (9600-10004)/(100 - 102)?
anonymous
  • 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
anonymous
  • anonymous
Is this for calculus or algebra?
anonymous
  • anonymous
calculus ab
anonymous
  • anonymous
and im starting to think this is wrong
anonymous
  • 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
anonymous
  • anonymous
Why do you think it is wrong?
anonymous
  • anonymous
because we didn't use an equation i was certain would be relevant
anonymous
  • anonymous
oh wait
anonymous
  • anonymous
you just proved me wrong :p
anonymous
  • anonymous
I changed the variables to X and Y but it is the same equation :)
anonymous
  • anonymous
okay and for part b do i just find the derivative at that point?
anonymous
  • anonymous
I assumed at first that it was an algebra class so I used X and Y, sorry for the confusion
anonymous
  • 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
anonymous
  • anonymous
thank's !!
anonymous
  • anonymous
You're welcome! Glad I could help!

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