Author Topic: Differentiation Question  (Read 3230 times)

Offline Tohru Kyo Sohma

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Re: Differentiation Question
« Reply #15 on: January 01, 2011, 02:44:58 pm »
Differentiate the equation. Set dy/dx = 0 and solve for x.

Determine if the stationary point is a minimum or maximum. Select the minimum point and plug it into the original equation.

This is the minimum cost.
sorry ari if ur getting fedup of me asking so much questions........but i got the answer.......thanks alot!! ;D

Offline Dibss

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Re: Differentiation Question
« Reply #16 on: January 01, 2011, 02:56:24 pm »
thank you so much wispher
i got it now........... ;)

Glad to help. (:

elemis

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Re: Differentiation Question
« Reply #17 on: January 01, 2011, 04:08:53 pm »
sorry ari if ur getting fedup of me asking so much questions........but i got the answer.......thanks alot!! ;D

No, I'm not fedup.


Offline Tohru Kyo Sohma

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Re: Differentiation Question
« Reply #18 on: January 01, 2011, 04:59:18 pm »

Offline Tohru Kyo Sohma

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Re: Differentiation Question
« Reply #19 on: January 01, 2011, 06:08:27 pm »
ok......so i hv yet another doubt;
a rectangle box with a lid is made from thin metal. its length is 2x cm and its width is x cm. if the box volume is 72 cm^3
a. show that the area of the metal used is equal to 4x^2 +216/x.
b. find the value of x so that the area A is minimum?

Offline Vin

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Re: Differentiation Question
« Reply #20 on: January 01, 2011, 07:48:15 pm »
l = 2x cm
w = x cm
V = 72 cm3

V = l * b * h
71 = 2x * x * h
h = 72/ 2x2

Area = 2 ( lb + lh + bh)
= 2 ( 2x * 72/ 2x2 + x * 72/ 2x2 + 2x * x )
= 2 ( 72/x + 36/x + 2x2 )
= 2 ( 108/x + 2x3 )
= 216/x + 4x2
or
4x2 + 216/x
Hence, proved.

Identify the domain.
4x2 >= 0
x>= 0
however, 1/x > 0 and not = 0
so domain is x belongs to positive integers.

dA/dx = 8x - 216/x2
substitute this as 0
you get x = 3
check whether it is the point of minimum.

Yes, it is, so x = 3 is the value where A is minimum.

Offline Tohru Kyo Sohma

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Re: Differentiation Question
« Reply #21 on: January 03, 2011, 03:29:36 pm »
l = 2x cm
w = x cm
V = 72 cm3

V = l * b * h
71 = 2x * x * h
h = 72/ 2x2

Area = 2 ( lb + lh + bh)
= 2 ( 2x * 72/ 2x2 + x * 72/ 2x2 + 2x * x )
= 2 ( 72/x + 36/x + 2x2 )
= 2 ( 108/x + 2x3 )
= 216/x + 4x2
or
4x2 + 216/x
Hence, proved.

Identify the domain.
4x2 >= 0
x>= 0
however, 1/x > 0 and not = 0
so domain is x belongs to positive integers.

dA/dx = 8x - 216/x2
substitute this as 0
you get x = 3
check whether it is the point of minimum.

Yes, it is, so x = 3 is the value where A is minimum.
thanks vin.... :D

Offline Dibss

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Re: Differentiation Question
« Reply #22 on: January 03, 2011, 03:38:52 pm »
l = 2x cm
w = x cm
V = 72 cm3
-
Yes, it is, so x = 3 is the value where A is minimum.

+Rep (:

elemis

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Re: Differentiation Question
« Reply #23 on: January 04, 2011, 07:05:46 am »
ok......so i hv yet another doubt;
a rectangle box with a lid is made from thin metal. its length is 2x cm and its width is x cm. if the box volume is 72 cm^3
a. show that the area of the metal used is equal to 4x^2 +216/x.
b. find the value of x so that the area A is minimum?

Essentially all of these questions follow the same general idea :

Differentiate equation

Set equal to zero

Solve to find max and min points

Use max and min points in original equation depending on what the question requires.

Offline Tohru Kyo Sohma

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Re: Differentiation Question
« Reply #24 on: January 05, 2011, 04:01:19 pm »
Essentially all of these questions follow the same general idea :

Differentiate equation

Set equal to zero

Solve to find max and min points

Use max and min points in original equation depending on what the question requires.
thanks ari
+rep

Offline Tohru Kyo Sohma

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Re: Differentiation Question
« Reply #25 on: January 06, 2011, 01:37:25 pm »
a new make of personel organizer costs $100 each to manufacture and market. market research indicates that the number, N thousand, of organizers that will be sold in the first year is given by; N=-1S+150, where $S is the selling price. the numbers which wll be sold at two particular selling prices are as given below
S                   N
120                30
140                10

a. express the profit per organizer in terms of S and hence show that the total profit in the first year is $T thousands, where T=-15000+250 S-S^2
b. find the selling price, which will produce the maximum possible total profit in the first year and find this total profit( you should show that this profit is maximum and not minimum)?

Offline astarmathsandphysics

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Re: Differentiation Question
« Reply #26 on: January 19, 2011, 10:21:55 pm »
here