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Multiplication Patterns

If X+y=4 find...

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If X+y=4 find the maximum value of x2y3

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Q. Find the maximum value of

3 x + 4 y

x > 0, y > 0

x^{2} y^{3} = 6

x + y = 28

then the maximum value of

x^{3} y^{4}

f (x) = x^{4} + y^{4} - x^{3} y^{2} - x^{2} y^{3} + 16 x y

. If x+y=2, what is the value of f(x)?

Q. Find the greatest value of

x^{2} y^{3}

subject to the conditions

3 x + 4 y = 5,

where x and y are positive numbers.

x + y = 3

, Show that the maximum value of

x^{2} y

4

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