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- marcelie

help please !!!!
Find the dimensions of the rectangular corral
producing the greatest enclosed area given 200 feet of
fencing.

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- marcelie

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- imqwerty

ok so its like-|dw:1442384074892:dw|
ur given that-
x+y=200
y=200-x
and the area should be maximum
area=x*y
area=x*(200-x)
area=200x-x^2
u can get the value of x for which the area will be max by differentiating the area equation which we got with respect to x and equating it to 0
so u get
\[\frac{ d}{ dx }(200x-x^2) =0\]
after differentiating u get-
200-2x=0
200=2x
x=100
and we know that y=200-x
so y=200-100
y=100
so the dimensions are x=100 and y=100
so basically if u are maximizing the area then the figure has to become a square even tho we are given that its a rectangle :)

- marcelie

how did u get 200x-x^2 =0

- imqwerty

we are given x+y=200 right
so after subtracting x from both sides u get
y=200-x -equation 1
nd we knw that the area is= x*y
area=x*y
put the value of y from equation 1 u get-
area=x*(200-x)
open the bracket u get-
area=200x-x^2 :)

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- marcelie

okay so then how did u get 200-2x =0 ?

- imqwerty

yes u get that after differentiating nd thats the way u do it :)

- marcelie

how do u do that ? by subtracting ?

- imqwerty

no
the differentiation of x^n with respect to x can be given as-
\[\frac{ d }{ dx }x^n =nx^\left( n-1 \right)\]
and if u have something like this -
ax^n + b where a and b are constants then the differentiation of this thing with respect to x will be-
\[\frac{ d }{ dx }(ax^n +b) =\frac{ d }{ dx }ax^n + \frac{ d }{ dx }b\]\[=anx^\left( n-1 \right)+0\]
basically differentiation of m with respect to n indicates the rate of change of m with respect to n
nd here we had a constant b nd we knw that constants are constants so differentiating it with respect to x gave us a 0
but ax^n is not a constant tho it has a but it has also got x^n which keeps changing so we get anx^(n-1) on differentiating it )
nd we used this to get 200-2x from 200x-x^2 :)

- marcelie

Got it now !! tyyy

- imqwerty

no prblm :)

- marcelie

how would i solve this one ?
Find the dimensions of the rectangular corral
producing the greatest enclosed area split into 3 pens of the
same size given 500 feet of fencing.

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