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# Calculus

Fri 12 Mar, 2004 10:47 pm
I need help in answering this question:

What is the largest possible product of two nonnegative numbers whose sum is 1?

Any ideas would be greatly appreciated.
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Type: Discussion • Score: 1 • Views: 613 • Replies: 3
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SCoates

1
Fri 12 Mar, 2004 11:13 pm
Is it not .5 and .5? I'm confused.
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Brandon9000

1
Sat 13 Mar, 2004 08:10 am
Differentiating x(1-x) and setting the result to zero to look for extrema, the result is x = .5.
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g day

1
Sun 21 Mar, 2004 07:36 pm
0.25

x + y = 1
x.y > 0

y = 1 - x

x.(1 - x) > 0 or x - x^2 > 0

Differentiate with respect to x to get turning points

f'(x) = 1 - 2x = 0 or 1 = 2x, x = 1/2

therefore y = 1 - 1/2 = 1/2 at the max point

Product = x.y = 1/2 * 1/2 = 1/4 or 0.25
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