Maximize B=5xy^2, where x and y are positive numbers such that x=y^2=6.

The maximum value of B is _?

The maximum value of B is 45

Corrected question;

Maximize B=5xy^2, where x and y are positive numbers such that x+y^2=6.

The maximum value of B is _?

Step-by-step explanation:

Given that;

B = 5xy^2 1

And;

x + y^2 = 6

y^2 = 6 - x 2

Substituting equation 2 to 1

B = 5x(6-x) = 30x - 5x^2

Maximizing B, at maximum point dB/dx = 0

dB/dx = 30 -10x = 0

30 = 10x

x = 30/10 = 3

x = 3

From equation 2;

y^2 = 6 - x = 6-3 = 3

y = √3

Maximum value of B is;

B = 5xy^2 = 5 × 3 × (√3)^2 = 45

B = 45

The maximum value of B is 45

Step-by-step explanation:

The numbers are:

and

Finally, the value of B is:

step-by-step explanation:

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