Calculus Question for 10pts PLEASE!!?

Question

I'm trying to figure this out for an upcoming test. Help would br greatly appreciated.

A DVD manufacture company finds its cost function is C(x) = 200√x + 600 dollars, where x is the number of DVD players produced. Estimate the cost of producing the 501th DVD player.

Answer 1

Unless you typed in the wrong question there is no calculus needed here.

To find the cost of the 501st dvd player you take the cost of producing 501 dvd players and subtract from it the cost of producing 500 dvd players.

c(501)-c(500)=200√501 + 600 - (200√500 + 600)
c(501)-c(500)=200(√501 - √500)
c(501)-c(500)=200(22.38303 - 22.36068)
c(501)-c(500)=200(0.02235)

c(501)-c(500)=4.47

Answer 2

I don't know if they want a plain or fancy answer. The plain answer is to substitute 501 in for x and solve, and then substitute 500 in for x and solve, and take the difference.

The fancy answer is to solve C(x) at 484 units, where x=22 and C(x)= 5000. Then you can expand a Taylor series about x=22 with one term
C'(x)dx appx = 200 /sqrt(x) * delta x.
Now we postulate that the term is linear, and can be averaged over a small interval to produce the cost per item.
Then for x=22 and delta x=19, the term is $ 171. Divide by 19 to get $9 for the 501th player.

Answer 3

I'm not sure if calculus comes into this question.

C(x) = 200√x + 600 dollars
C(501) = 200√(501) + 600 dollars
C(x) = 200(22∙383 029 29..) + 600 dollars
C(x) = 4476∙605 857.. + 600 dollars
C(x) = 5076∙605 857 dollars

This is for the production of 501 players.
If you just want the last one, subtract it from the cost of the first 500.

Answer 4

C(501) = 200.√501 + 600
C(501) = 5076.61
C(500) = 200√500 + 600
C(500) = 5072.14
Cost of producing the 501st article = $ 4.47

Answer 5

It is C(501) - C(500) = 200*(sqrt(501) - sqrt(500)) = 4.47 $.