This blog created by Fariel Mohan is to assist MATH110D students in understanding foundational mathematical concepts.
Saturday, March 1, 2008
Test the application of derivatives
A small company makes x hand-painted tiles daily at a cost of C(x) = 125 + 30x + 2x^3/2 dollars. What daily production level minimizes the average cost—i.e., the cost per tile?
the production level is the amount of tiles that is produced for the day. therefore if less tiles are produced then the average cost of tiles would increase, comprende
To solve: you bring the x term to the top and make the power negative. Then u multiply the negative power by the term in front the x. so u get -1x. Then y minus 1 from the negative power. so u get -3.
Im abit confused!!! To find the cost per tile jus substitute 1 into the equation so C(1) = 125 + 30(1) + 2(1)^3/2 = 157.83 Did i have to do dat??? Wats next???
well, it is established that you must differentiate the equation (dC/dx), to find the rate and substitute a value into the equation, right? can somebody please explain the production level part,or disenclined to acquiest my request?
U will have to differentiate the equation dC/dx== 125 + 30x + 2x(3/2) Thats all i know. But i think that yoshi is tring to say that if u have less tiles produced, the average cost will increse. that does not make any sence because if u are making more tile the cost will increase and the average cost will increse.
but i think u got that from taking the amount of money and dividing by the number of tiles. so if u get more tiles u will have to divided hence why u get a smaller.If thats the case then the cost will increase ant the average cost will decrease. correct me if I am wrong please.?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?
let me see, hmmmmmmmm... i think in this question you hav to solve it using deffrentiation...as brainiac did with c(x)= 125 + 30x + 2x(3/2) dc/dx = 30 + 3x(1/2)
every1 is sayin2 2 differentiate but cokebaby says u could substitue which 1 is correct. an where do u go from after differentiating. dc/dx=30+(3/2)2x^1/2. wat is the next step from here.
arite if i get dis rite..x is de number of tiles produced in a day and the question wants us to find a value for x that would minimize the average cost rite ??rite ?
so if de more tiles you have (now this is where im confused) would C(x) not increase? but the question is..what does C(x) represents? note- i a even get into de equation part as yet eah i jus trying to analyse this question..so anyone help ah fadda out nah..cuz i a really get de driff.
but wait nah ent C(x) is just a representation of what is on the y axis? so therefore C(x) and f(x) or Z(x) or [de hole alphabet(x)] does not make a difference?
to tell you d truth i odnt c how you r goin to use derivatives to find prodution level, i am thinking along the same line as coke baby with wat he suggested by substitueing i into the eq
to violet: C (x) is the cost of daily production for the tiles. the derivative will be the change in the cost per tile. since all the tiles are priced the same the change in cost per tile will be the cost of a tile. understand?
cpucat i think you're thinking about the question too hard. You simply looking at the cost of one tile as a factor of he daily cost. the cost of the tiles do not change.
"What daily production level minimizes the average cost" anybody know wat that suppose to mean?????? does this questiion have to do with small changes????
wat if we differentiate the function C(x) and substitute 1 in to the differential? Wats wrong with dat??? Remember when we diffrentiate and substitute 1 we are finding the rate of change per tile. We dont know the amount of tiles produced in a particular day so we have to work wit wat we have. that is the cost of 1 tile and the rate of change of 1 tile....im stick.. i tink im going in the right direction!!!! Anyone care to add.
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46 comments:
firstly is that 2 multiply by 3/2 or
2x multiply by 3/2
the production level minimizes in its average cost according to the root of the x values.i.e. the differential of the function C(x).
You must differentiate the question first by finding dc/dx = 125 + 30x + 2x(3/2)
which is
dc/dx = 30 + 3x(1/2)
Yoshi i dont understand wat u are saying bout the root of the values x?
yoshi you lost me. could you explain the production level thing
Well x being the number of tiles daily
the cost is C(x) =125+30x+2x^3/2dollars daily
I believe we are asked to find the rate of production of tiles
the production level is the amount of tiles that is produced for the day. therefore if less tiles are produced then the average cost of tiles would increase, comprende
Na C(x) means f(x)
so it should be rate of change of x
root of x means the amount of tiles produced
Ok yoshi i think i understand now
so brainiac, how do you differentiate a power that is not a positive integer
so to could be dt/dx
3^1/2+30=........(calculate it)
I think
and also for fractions.
Cp3:
you said that you are finding the rate of change of C(x) rite. I'm confuse wen you said that C(x) is
f(x) wat do u mean by that?
Cp3 how u realy get dt/dx instead now????? Plz comment
cp3 hold up in differentiation C(x) means C(x) not f(x).
and how did u get dt/dx
OK the question wants u to find the rate of production of tiles so it must be dt/dx dt being the change in time
Yoshi:
You mean a question like 1/x(2).
To solve:
you bring the x term to the top and make the power negative.
Then u multiply the negative power by the term in front the x.
so u get -1x.
Then y minus 1 from the negative power.
so u get -3.
Then the answer is -1x(-3) rite.
Im abit confused!!! To find the cost per tile jus substitute 1 into the equation so
C(1) = 125 + 30(1) + 2(1)^3/2
= 157.83
Did i have to do dat??? Wats next???
well, it is established that you must differentiate the equation (dC/dx), to find the rate and substitute a value into the equation, right? can somebody please explain the production level part,or disenclined to acquiest my request?
U will have to differentiate the equation dC/dx== 125 + 30x + 2x(3/2)
Thats all i know.
But i think that yoshi is tring to say that if u have less tiles produced, the average cost will increse. that does not make any sence because if u are making more tile the cost will increase and the average cost will increse.
but i think u got that from taking the amount of money and dividing by the number of tiles. so if u get more tiles u will have to divided hence why u get a smaller.If thats the case then the cost will increase ant the average cost will decrease. correct me if I am wrong please.?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?
by defferneciating this equation in terms of dc/dx as braniac righfully said you will end up with 3o + 30x(3/2)
but when yoshi talks about the production level I am lossed?? Waht do yu do next??
let me see, hmmmmmmmm... i think in this question you hav to solve it using deffrentiation...as brainiac did with
c(x)= 125 + 30x + 2x(3/2)
dc/dx = 30 + 3x(1/2)
i don't think it is correct though, because we didn,t actually find the cost of an individual tile....how do we do this???
hmmmmmm???
I have always disliked real life applications and it some time to try and figure it out. Is all you have to do is differentiate C(x)
every1 is sayin2 2 differentiate but cokebaby says u could substitue which 1 is correct.
an where do u go from after differentiating.
dc/dx=30+(3/2)2x^1/2.
wat is the next step from here.
Right I'm back
pussinboots at this point 3x^1/2+30 I believe u Substitute x=1
which should give u
30+3x^1/2
30+3(1^1/2)
33
cp3
i understand from
30 + 3x^(1/2)
but how did you know that x=1?
does the question state that because half the question is overwrite by the title...
yoshi
please xplain what is an interger..u said
"so brainiac, how do you differentiate a power that is not a positive integer"
arite if i get dis rite..x is de number of tiles produced in a day and the question wants us to find a value for x that would minimize the average cost rite ??rite ?
so if de more tiles you have (now this is where im confused) would
C(x) not increase? but the question is..what does C(x) represents? note- i a even get into de equation part as yet eah i jus trying to analyse this question..so anyone help ah fadda out nah..cuz i a really get de driff.
but wait nah ent C(x) is just a representation of what is on the y axis? so therefore C(x) and f(x) or Z(x) or [de hole alphabet(x)] does not make a difference?
to tell you d truth i odnt c how you r goin to use derivatives to find prodution level, i am thinking along the same line as coke baby with wat he suggested by substitueing i into the eq
to violet:
C (x) is the cost of daily production for the tiles. the derivative will be the change in the cost per tile. since all the tiles are priced the same the change in cost per tile will be the cost of a tile. understand?
cpucat i think you're thinking about the question too hard. You simply looking at the cost of one tile as a factor of he daily cost. the cost of the tiles do not change.
hey cp3, when you first substiuted x = 1,,, won't that change part of the equation?
or somebody tell me if i'm going wrong.
i get dc/dx = 30+(3/2) 2x^1/2... whew!
i think i on track with pussinboots but as i said before... why substitute x = 1?
dc/dx = 125 + 30x + 2x(3/2)
dc/dx = 30 + 3x(1/2)
First you need to differentiate the equation, you will get
dc/dx = 30+(3/2) 2x^1/2 but to find the cost per tile i am not sure how to do that.
i understand when everyone get
30+3x^1/2
so what you all doing after this value is obtained?
"What daily production level minimizes the average cost" anybody know wat that suppose to mean?????? does this questiion have to do with small changes????
wat if we differentiate the function C(x) and substitute 1 in to the differential? Wats wrong with dat??? Remember when we diffrentiate and substitute 1 we are finding the rate of change per tile. We dont know the amount of tiles produced in a particular day so we have to work wit wat we have. that is the cost of 1 tile and the rate of change of 1 tile....im stick.. i tink im going in the right direction!!!! Anyone care to add.
i agree with you cokebaby we have to use what we have because we do not know the amount of tiles produced in one day.
but inspite of this we were only asked to find the cost of each tile so you do not need to buss ur brain for this question.
so all u have to do is basically differnciate and substitute and you will get ur ans i think am i right????
diferrentiation AGAIN dp being the production level dc cost of tile
dp/dc is the rate of change of cost with respect to the production level
critical what is derivitives used in real life, what is the purpose of it.
the question said that x tiles cost 125+30x+2x^3 therefore if you want to find for 1 tile you have to substitute x=1 resulting
125+30(1)+2(1)^3
=161
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