Maximizing Product of Two Parts of 13
To find two numbers that can be multiplied to give the maximum product when added together equals 13, we need to follow these steps:

Step 1: Understanding the Problem
We are looking for two numbers x and 13-x such that their product is maximum.

Step 2: Calculating the Product
Let the two numbers be x and 13-x. The product P is given by P = x(13-x).

Step 3: Maximizing the Product
To maximize the product, we need to find the derivative of P with respect to x and set it equal to zero.

Step 4: Solving for x
Differentiating P = x(13-x) with respect to x, we get dP/dx = 13 - 2x. Setting dP/dx equal to zero, we get 13 - 2x = 0, which gives x = 6.5.

Step 5: Finding the Numbers
Therefore, the two numbers that yield the maximum product are 6.5 and 6.5 (since 13-6.5 = 6.5).

Step 6: Checking the Product
The product of 6.5 and 6.5 is 42.25, which is the maximum product that can be obtained by dividing 13 into two parts.
By following these steps, we have determined that dividing 13 into two parts, 6.5 and 6.5, will result in the maximum product of 42.25.