# Answer on Calculus Question for Marcel

Question #2357

Find the maximum and minimum values of the function f(x,y) = x2 ‐2y subject to the constraint

that x2 + y2 = 9 and please show calculations

that x2 + y2 = 9 and please show calculations

Expert's answer

We should use Lagrange multipliers and Extreme value theorem. Let's construct the system of equations:

2x = 2λ x;

-2 = 2λ y;

x

Hence: λ = 1, y = -1, x

The function has one extreme value:

f(x,y) = 8 + 2 = 10.

f(√5, 2) = 5 - 2 = 3.

Thus f(x,y) = 10 is the maximum of the given function subject to constraint that x

2x = 2λ x;

-2 = 2λ y;

x

^{2}+ y^{2}= 9.Hence: λ = 1, y = -1, x

^{2}= 8.The function has one extreme value:

f(x,y) = 8 + 2 = 10.

f(√5, 2) = 5 - 2 = 3.

Thus f(x,y) = 10 is the maximum of the given function subject to constraint that x

^{2}+ y^{2}= 9.Need a fast expert's response?

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