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The sum of two nonnegative numbers is 50. What is the maximum value of the product of these two numbers ?

Sagot :

Answer:

625

Step-by-step explanation:

Let two number be x and (50-x).

The product of numbers be x(50-x).

P = 50x-x²

For maximizing the product,

[tex]\dfrac{dP}{dx}=0\\\\\dfrac{d}{dx}(50x-x^2)=0\\\\50-2x=0\\\\50=2x\\\\x=25[/tex]

So, the maximum product, P = 50(25)-(25)²

P = 625

Hence, the maximum value of the product of these two numbers is 625.

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