Final answer:
To find the two numbers whose sum is fifteen and whose product is a maximum, we need to use the concept of maximums and minimums in calculus.
Step-by-step explanation:
To find the two numbers whose sum is fifteen and whose product is a maximum, we need to use the concept of maximums and minimums in calculus. Let's assume the two numbers are x and 15-x. The product of these two numbers is given by f(x) = x(15-x). To find the maximum value of f(x), we need to take the derivative and set it equal to zero. By solving this equation, we can find the value of x that maximizes the product. Substituting this value back into the equation will give us the other number.
For example, if x = 7.5, then the two numbers are 7.5 and 7.5. Their sum is fifteen, and their product is 56.25, which is the maximum value.