# 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?

##### 2 Answers

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#

#2x= 50#

#x = 25#

Which means that the maximum product will happen when

Hopefully this helps!

#### Answer:

See below.

#### Explanation:

Here the extremum point problem is equivalent to this one.

Given the function

determine

Choosing

but tangency implies one solution hence

and finally

b)