Question

What two nonnegative real numbers with a sum of have the largest possible​ product?.

Answer 1

The two non negative real numbers with a sum of 60 that have the largest possible​ product are 30 and 30.

What are non negative numbers?

Non-negative numbers are those that are either zero or positive (remember that 0 and 0 are the same). An integer that is either positive or zero is considered a non-negative integer. It is the result of adding all the natural numbers together with zero. It can be defined as the set "0, 1, 2, 3,...," and is also known as Z.

An integer that is either positive or zero is considered a non-negative integer.

Let us assume the two non negative numbers are $x$ and $y$.

According to the question,

Sum of two non negative numbers = 60

⇒ $x+y=60$

⇒ $y=60-x$

Their product will be given as,

⇒ $P=xy$

⇒ $P=x(60-x)$

⇒ $P=60x-x^2$

For the product to be largest $P'(x)=0$

⇒ $P'(x) = 60-2x$

⇒ $60-2x=0$

⇒ $2x=60$

⇒ $x=30$

Now, for the value of $y$

⇒ $y=60-x$

⇒ $y=60-30$

⇒ $y=30$

Therefore, the two non negative numbers are 30, 30.

To know more about the non negative numbers..........

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