divide the number 20 into two parts such that their product is maximum
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let x and 20-x be the parts
product =x(20-x)=x²-20x
dp/dx=2x-20
put=dp/dx=0
2x-20=0
2x=20
x=10
d²p/dx²=2
now, d²p/dx² is positive when x=10
so 10,10 is two parts of 20 and their product is maximum
product =x(20-x)=x²-20x
dp/dx=2x-20
put=dp/dx=0
2x-20=0
2x=20
x=10
d²p/dx²=2
now, d²p/dx² is positive when x=10
so 10,10 is two parts of 20 and their product is maximum
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