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We are given the following information:
the sum of the first number cubed and the second number is 500
their product is a maximum
We are looking for the 2 missing numbers.
To answer this, let's represent the two numbers as x and w.
From the given, we can form the following equation:
We can then express y as:
We can express their product as:
To find the maximum value of x, let's solve for the derivative of -x^4 + 500 x.
Then we solve for the value of x where f'(x) = 0.
Then we use x = 5 to solve for the second number, w.
Therefore, the two numbers are 5 and 375.