Divide a number 100 into two parts such that their product is maximum.

Let the two parts be x and (100-x)Product,P=x(100-x)=100x-x2For P to be maximum or minimum,dPdx=100-2x=0x=50d2Pdx2=-2i.e. P is maximum at x =50Dividing equally the two parts are (50,50)