what two nonnegative real numbers with a sum of 64 have the largest possib let x be one of the numbers and…

what two nonnegative real numbers with a sum of 64 have the largest possib let x be one of the numbers and let p be the product of the two numbers. writ p = 64x - x² (type an expression.) the interval of interest of the objective function is . (simplify your answer. type your answer in interval notation.)

what two nonnegative real numbers with a sum of 64 have the largest possib let x be one of the numbers and let p be the product of the two numbers. writ p = 64x - x² (type an expression.) the interval of interest of the objective function is . (simplify your answer. type your answer in interval notation.)

Answer

Explanation:

Step1: Define the variables

Let one number be $x$, the other is $64 - x$, and $P=x(64 - x)=64x - x^{2}$. Since the numbers are non - negative, $x\geq0$ and $64 - x\geq0$.

Step2: Solve the inequalities for the interval

From $x\geq0$ and $64 - x\geq0$ (which is equivalent to $x\leq64$), the interval of $x$ is $[0,64]$.

Answer:

$[0,64]$