what two nonnegative real numbers with a sum of 64 have the largest possible product? let x be one of the…

what two nonnegative real numbers with a sum of 64 have the largest possible product? let x be one of the numbers and let p be the product of the two numbers. write the objective function in terms of x. p = 64x - x² (type an expression.) the interval of interest of the objective function is 0,64. (simplify your answer. type your answer in interval notation.) the numbers that have a sum of 64 and have the largest possible product are (use a comma to separate answers as needed.)

what two nonnegative real numbers with a sum of 64 have the largest possible product? let x be one of the numbers and let p be the product of the two numbers. write the objective function in terms of x. p = 64x - x² (type an expression.) the interval of interest of the objective function is 0,64. (simplify your answer. type your answer in interval notation.) the numbers that have a sum of 64 and have the largest possible product are (use a comma to separate answers as needed.)

Answer

Explanation:

Step1: Identify the function type

The objective function $P = 64x - x^{2}$ is a quadratic - function of the form $y = ax^{2}+bx + c$ where $a=-1$, $b = 64$ and $c = 0$.

Step2: Find the vertex of the quadratic function

The x - coordinate of the vertex of a quadratic function $y = ax^{2}+bx + c$ is given by $x=-\frac{b}{2a}$. Substituting $a=-1$ and $b = 64$ into the formula, we have $x=-\frac{64}{2\times(-1)}=\frac{-64}{-2}=32$.

Step3: Find the other number

Since the sum of the two non - negative real numbers is 64 and one number is $x = 32$, the other number is also $64 - 32=32$.

Answer:

32, 32