The sum of two positive numbers is 20. find the numbers if their product is maximum

Text Solution

6,1415,512,810,10

Answer : C

Solution : Let the numbers are x and y <br> So x+y =20 Let `P=x^(2)y^(3)` <br> `=x^(2)(20-x)^(3)` <br> Differntiating w.r.t.x <br> `(dp)/(dx)=0` for maxima or minima <br> So , `(20-x)^(2) [40x -5x^(2)2(20-x)(-1)]` <br> `(dp)/(dx)=0` for maxima or minima <br> So `(20-x^(2))[40x-5x^(2)]=0` <br> `rarr (20-x)^(2)xx(x)(40-5x)=0 rarr x = 20,0,8` <br> `(d^(2)p)/(dx^(2))_(x=20)=0`

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