Question

Examine The Function For Relative Extrema.

G(X,Y)=2−∣X∣−∣Y∣
A relative minimum (x,y,z)=
B relative maximum (x,y,z)=
C saddle point (x,y,z)=

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Answer 1

To determine the function for relative extrema, examine the first and second derivatives. The function G(x,y) = 2 - |x| - |y| has a relative maximum at (x,y) = B.

Step-by-step explanation:

To determine the function for relative extrema, we need to examine the first and second derivatives of the function. If the first derivative changes sign from positive to negative, we have a relative maximum. If the first derivative changes sign from negative to positive, we have a relative minimum. If the second derivative is zero, we have a saddle point.

For the function G(x,y) = 2 - |x| - |y|, let's first examine the first derivative:

G'(x,y) = -1 (when x > 0) or G'(x,y) = 1 (when x < 0)

Since the sign of the first derivative changes from positive to negative as we move from x < 0 to x > 0, we have a relative maximum at (x,y) = B. There is no saddle point.