Answer:
625
Step-by-step explanation:
Let two number be x and (50-x).
The product of numbers be x(50-x).
P = 50x-x²
For maximizing the product,
[tex]\dfrac{dP}{dx}=0\\\\\dfrac{d}{dx}(50x-x^2)=0\\\\50-2x=0\\\\50=2x\\\\x=25[/tex]
So, the maximum product, P = 50(25)-(25)²
P = 625
Hence, the maximum value of the product of these two numbers is 625.
