Finding the minimum product of two numbers whose difference is 8, HOW?
This is the solution in my textbook:
"The quantity to be minimized is the product, p, of two numbers.
Let one number be n.
Since the difference between the two numbers is 8, the other number can be represented by n-8 or n+8.
Either expression can be used. We will use n-8.
p = n * (n-8)
...
"
Now the thing I don't get is that why do we need P? Why do we multiply the two numbers?
the problem wants you to find the minimum product of two numbers whose difference is 8
the product of two numbers is the result when you multiply the two numbers ...
the product = (first number) times (the second number)
P = n(n-8)
note that the graph of P = n(n-8) is a parabola ... the vertex of the parabola is the location of the minimum product.
what do you know about finding the vertex of a parabolic graph?