Question

find two positive numbers x and y.such that x+y=60 and xy^3 is maximum​

Answer 1

Answer:

Let P=xy3

It is given that x+y=60

⇒x=60−y

P=(60−y)y3   [Putting value of x]

    =60y3−y4

⇒dydP=180y2−4y3

dy2d2P=360y−12y2

For maximum or minimum values of y, P we have

dydP=0

⇒180y2−4y3=0

⇒4y2(45−y)=0

⇒y=0    45−y=0    y=45

Now (dy2d2P)y=45=360×45−12(45)2

                                 =12×45−(30−45)

           then the no. is 15 and 45