Respuesta :

caylus
Hello,

x+y²=4==>y²=4-x
Max(Q=xy²)=Max(Q=x(4-x))=Max(Q=4x-x²)

Q'(x)=4-2x =0
==>x=4/2=2 ==>y²=4-2=2==>y=√2 since y>0

Q''(x)=-2==>a maximum.

Maxima of Q = xy^2 will be at x = 2 and y = √2.

What is maxima of a function?

Maxima of a function means what can be the maximum possible value of the function.

It is given that-

Q = xy^2, where x and y are positive numbers

and,

x + y^2 = 4

⇒ y^2 = 4 - x

So, Q can be written as-

Q = x(4 -x)

or, Q = 4x -x^2

Differentiating Q w.r.to x we get-

Q' = 4 - 2x

Now, For maximum value of Q

Q' = 0

⇒ 4 - 2x = 0

⇒  - 2x = -4

⇒      x = 2

Putting the Value of x in y. We get,

y^2 = 4 - 2

⇒  y^2 = 2

⇒ y = √2  

Again differentiating Q w.r.to x. We have

   Q'' = -2

is negative.

Since x and y to be positive, We conclude that maximum point is-

x = 2

y = √2  

Hence, maxima of Q = xy^2 will be at x = 2 and y = √2.

More about Maxima :

https://brainly.com/question/13736844

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