Differentiation Question

[Tohru Kyo Sohma]

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!!

[Dibss]

thank you so much wispher
i got it now...........

Glad to help. (:

[elemis]

sorry ari if ur getting fedup of me asking so much questions........but i got the answer.......thanks alot!!

No, I'm not fedup.

[Tohru Kyo Sohma]

No, I'm not fedup.

cool
 

[Tohru Kyo Sohma]

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?

[Vin]

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.

[Tohru Kyo Sohma]

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....

[Dibss]

l = 2x cm
w = x cm
V = 72 cm3
-
Yes, it is, so x = 3 is the value where A is minimum.

+Rep (:

[elemis]

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.

[Tohru Kyo Sohma]

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

[Tohru Kyo Sohma]

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)?

[astarmathsandphysics]

here