微分differentiation

Let x be one of the part, so the other part is (50 - x). The product P is :
= x(50 - x)
= 50x - x^2
dP/dx = 50 - 2x
When dP/dx = 0, then x = 25, and d^2P/dx^2 = -2, so x = 25 is max.
Therefore when 50 is divided into 2 equal parts the product is maximum.
ie. 50 divided into 25 and 25, the product is 625, the maximum.