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# Differentiation Question. HELP NEEDED URGENTLY! watch

1. This is really frustrating me!!

Q: Two real numbers x and y are such that 2x+y=100.
find the maximum value of the product of the two numbers.

2. y=100-2x
x=(100-y)/2

x*y=?

Rerrange to get only x on RHS...
3. I'm sorry but I can't see how this helps?
5. (Original post by crimsonmist2)
How did you work that out? it would be very helpful if you could share your wisdom. thanks.
6. 2x+y=100
if you multiply the whole thing by x,
2x^2 + yx = 100x
so
yx= 100x - 2x^2
therefore yx is a function of x
so if you differentiate yx with resp to x
its equal to: 100-4x
so to find maxima put that = 0 and solve
you get x= 25
to find the value of xy, you put x= 25 into 100x- 2x^2
and you get 1250
7. ok?
8. Thank you very much, makes perfect sense!
10. the whole reason i put this post up was to get help with doing the question. i didnt just ask for the answer.
if you just told me what to do without doing it, that would have been great.
giving just the answer was no help at all!
11. x.y = x(100-2x)
= -2x^2 + 100x
= -2(x-25)^2 +1250

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Updated: February 6, 2010
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