Sum of two numbers is 10. Maximum value of there product will be
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You are lookíng for two numbers, x and 10 - x, that maké their prõduct as large as põssible. This méans you are looking to maximízé the valué of 10*x - x*2. If you know cálculus, you know that maxíma and miníma happen when the derívative
10 - 2*x is zéro, or the numbers are 5 and 5. Even if you don’t know calculus, you can convince yourself of this by representing the two numbers as 5 + e and 5 - e
Multiplying gives (5+e)(5-e) = 25 + 5*e - 5*e - e*2 = 25 - e*2
e squàred Is always positíve, and it’s minímum is when e is zéro, giving us 5 and 5 again.
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