Question

The cost of manufacturing x items is given by C(x) = 0.02x^2 + 20x + 1800. Find the marginal cost function. Compuare the marginal cost at x = 2- to the actual cost of producing the 20th item.

Answer 1

@UnkleRhaukus can u help?

Answer 2

@amistre64 @Best_Mathematician can u help?

Answer 3

ok

Answer 4

marginal cost is the derivative of cost

Answer 5

so i should take the derivative of that?

Answer 6

yes

Answer 7

okay

Answer 8

actual cost of nth item: C(n) - C(n-1)

marginal cost of nth item: C'(n)

Answer 9

okay got it

Answer 10

ait is this derivatives

Answer 11

Best mistook 2- as something other than a typo ... but was on the right track

Answer 12

yea its positive 2 sorry

Answer 13

the marginal cost of the 20th item is, the rate of change in cost of the 20th item

actual cost is the extra amount that the 20th item costs compared to the actual cost of the 19th item

Answer 14

so marginal cost and actual cost r 2 different things

Answer 15

so after i find the derivative i should plug in 20 into C'(x) to find the marginal cost for 20th items.??

Answer 16

thats correct, the word marginal in finance relates to derivatives

Answer 17

yes, C'(20) = marginal cost at x=20

Answer 18

okay

Answer 19

got it...not a business major but i do have great interest in business

Answer 20

so that would be my actual cost or?

Answer 21

for actual cost simply plug in values for marginal cost plugin values in derivatives

Answer 22

okay

Answer 23

\[actual~cost=\frac{C(b)-C(a)}{b-a}\]
\[marginal~cost=\lim_{a\to b}\frac{C(b)-C(a)}{b-a}\]

Answer 24

okay i see

Answer 25

so its asking me for the cost function...
For the cost function in problem 2, find the value of x which minimized the average cost

Answer 26

@amistre64 @Best_Mathematician @electrokid can u help with the second question?

Answer 27

new question => new post

Answer 28

ok