If the cost of manufacturing x items is c(x) = x^3 + 20x^2 + 90x + 15 , find the marginal cost function and compare the marginal cost at x = 50 and the actual cost of manufacturing the 50th item.

Question

If the cost of manufacturing x items is c(x) = x^3 + 20x^2 + 90x + 15  , find the marginal cost function and compare the marginal cost at x = 50 and the actual cost of manufacturing the 50th item.

anonymous · Answer

@amistre64  can u help?

amistre64 · Answer

the word marginal should give you the idea of a derivative

anonymous · Answer

okay

anonymous · Answer

so how would i do that will it be likfe this c'(50) = x^3 + 20x^2 + 90x + 15  or?

amistre64 · Answer

yes, but youd actually need to take the derivative of the right hand side ....

anonymous · Answer

so the derivative of x^3 + 20x^2 + 90x + 15?

amistre64 · Answer

yes, find the derivative of: x^3 + 20x^2 + 90x + 15, which will then be your marginal cost function

 i recall a question similar to this awhile back that needed to be divided by x; not too sure if we need that here tho

anonymous · Answer

ok i got 3x^2 + 40x + 90

amistre64 · Answer

that is a good marginal cost function; and since there is no word "average" being tossed about the divide by x is not an issue http://homepage.smc.edu/wong_betty/math28/pdf%20files/C11%20SSM%20Ch%203%20pt%205.pdf

anonymous · Answer

ok

amistre64 · Answer

C(50) - C(49) should be the exact cost

whereas C'(50) is the marginal cost value

anonymous · Answer

okay

anonymous · Answer

so i substitute those into the derivative or ??

amistre64 · Answer

you have a cost function C(x); find:  C(50) - C(49)

you have a marginal cost function as C'(x), find:  C'(50)

and compare the values

anonymous · Answer

so i do that with x^3 + 20x^2 + 90x + 15 or 3x^2 + 40x + 90

amistre64 · Answer

what is your C(x) function?

anonymous · Answer

x^3 + 20x^2 + 90x + 15

amistre64 · Answer

and when x=50, what value does that produce?

anonymous · Answer

ok i got 1125015

amistre64 · Answer

now, what is the value when x=49?

anonymous · Answer

i got 1082474

amistre64 · Answer

good, now subtract the value for 50, from the value for 49; what do we end up with?

anonymous · Answer

i get 42541

amistre64 · Answer

1125015
-1082474 
----------
      42541  is what i get too

amistre64 · Answer

now, what is our C"(x) function?

amistre64 · Answer

err, C'(x) function that is

anonymous · Answer

its 3x^2 + 40x + 90

amistre64 · Answer

and what value do we get for that function when x=50?

anonymous · Answer

i get 24590

amistre64 · Answer

now it asks you to compare the results

    actual cost is:  42541
marginal cost is:  24590

what it means by compare, i havent a clue

anonymous · Answer

well the actual cost is bigger? i don't know.. :/

amistre64 · Answer

lol, that would seem fine to me, but im not the one grading it so i cant really say what it means to compare them for ...

anonymous · Answer

okay thanks for the help

amistre64 · Answer

good luck :)