Qualification > Math
Differentiation Question
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:
--- Quote from: ~Vin~ 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.
--- End quote ---
thanks vin.... :D
Dibss:
--- Quote from: ~Vin~ on January 01, 2011, 07:48:15 pm ---l = 2x cm
w = x cm
V = 72 cm3
-
Yes, it is, so x = 3 is the value where A is minimum.
--- End quote ---
+Rep (:
elemis:
--- Quote from: mimiswift 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?
--- End quote ---
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:
--- Quote from: Ari Ben Canaan on January 04, 2011, 07:05:46 am ---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.
--- End quote ---
thanks ari
+rep
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