X+y=50 which x and y are two positive numbers (a)for which numbers x is the product of the two numbers an increasing function of x (b)what is the maximum value of their product?
We can see that
#p(x) = xy = x(50 - x) = 50x - x^2#
Now we take the derivative.
#p'(x) = 50 - 2x#
Take the derivative at
#0 = 50 - 2x#
#x = 25#
Which means that the maximum product will happen when
Hopefully this helps!
Here the extremum point problem is equivalent to this one.
Given the function
but tangency implies one solution hence