Answer
The product of two positive numbers can be given by the following function:
$P(x)$ = $60x - x^{2}$, $x\gt0$
Work Step by Step
To find a function that expresses $P$, the product of two numbers, we need to set up the equation:
$P(x)$ = $xy$
We also know that the sum of those two positive numbers is $60$, so we can set up an equation for this statement as well:
$x + y$ = 60
We can solve for $y$ to get $y$ in terms of $x$. We subtract x from both sides:
$y$ = $60 - x$
Now, we can plug in what we got for $y$ into the equation to find the product of the two numbers:
$P(x)$ = $(x)(60 - x)$
We then distribute the terms to simplify the function:
$P(x)$ = $60x - x^{2}$
