need help with maximum and minimum problems (1 Viewer)

[koizora]

i haven't done it before so just a bit confusing ...

1)
the perimeter of a rectangle is 80 metres and its length is x metres. what are the dimensions of the rectangle that enclose the maximum area?

2) the area of a rectangle is 100 cm2 and one of its sides is x cm. find the minimum perimeter possible?

3) find the maximum product of two numbers whose sum is 25. let the first number be x


thanks 4 ur helping

 

[shuning]

回复: need help with maximum and minimum problems

1) the max area when its a square

 

[shuning]

回复: need help with maximum and minimum problems

sry im really lazy 2 finish it 4 u. but u should know what to do from now on LOL

Q2




max min P when
dont forget to check.

 

[shuning]

回复: need help with maximum and minimum problems

Q3
N = x (25-x)




for max or min N

again like last Q

 

[scardizzle]

i haven't done it before so just a bit confusing ...

1)
the perimeter of a rectangle is 80 metres and its length is x metres. what are the dimensions of the rectangle that enclose the maximum area?

2) the area of a rectangle is 100 cm2 and one of its sides is x cm. find the minimum perimeter possible?

3) find the maximum product of two numbers whose sum is 25. let the first number be x


thanks 4 ur helping

2) xy = 100
therefore y= 100/x - eq'n 1
2x + 2y = P(perimeter) - eq'n 2

sub 1 into 2

2x + 200/x = P

therefore P' = 2 - 200/x^2

let P' = 0 for stat pts

therefore 0 = 2 - 200/x^2

therefore 200 = 2x^2

therefore x = 10

P" = 400/x^3

when x = 10 P" > 0 therefore x = 10 is a minimum

sub back into P

20 + 200/10 = 40

therefore min perimeter is 40cm^2

Same method for the other 2 pretty easy once you get the hang of it find 2

expressions, sub them together, differentiate, find stat pts

rinse, lather, wash, repeat

 

[Aerath]

 

[shuning]

回复: Re: need help with maximum and minimum problems

^ wow gw ^^

 

[koizora]

thank you very much!!!
i got it now