Max/Min Problem (1 Viewer)

[>> Lisa <<]

Hey i was wondering if anyone could help me out with this problem:

divide 20 into two parts such that the product of the parts is a maximum


the answer is 10 and 10 but how?


could some one help me out please

thanks in advance

 

[nick1048]

20 = x + (20 - x) --> This is where u divide 20 into two parts
now, let the product = y

y=x.(20-x)
= -x^2 + 20x --> From here differentiate
y' = -2x + 20
when y' = 0
0 = -2x + 20
-20 = -2x
.: x = 10

 

[Meldrum]

20 = x + (20 - x) --> This is where u divide 20 into two parts
now, let the product = y

y=x.(20-x)
= -x^2 + 20x --> From here differentiate
y' = -2x + 20
when y' = 0
0 = -2x + 20
-20 = -2x
.: x = 10

I hate to do a bit of raining here, but the next step is to test *IF* it is a maximum:

f''(x) = -2
-2<0 - therefore, a maximum exists at 10.

 

[KFunk]

I hate those tests. The leading coefficient was negative... proof enough...

 

[nick1048]

exactly. If you don't know the trends of simplistic functions like that, then you obviously haven't done curve sketching in maths lol. But pedantically, your right Gavrillo.