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if (1, 3) is a critical point of f(x, y), and f xx (1, 3)=-2, f xy (1, 3)=-3, f

ID: 2868094 • Letter: I

Question

if (1, 3) is a critical point of f(x, y), and fxx(1, 3)=-2, fxy(1, 3)=-3, fyy(1, 3)=-6, what is the value of D at (1, 3) and what can you say about the f(1, 3) based on using the Second Derivatives Test?

D=3 and f(1, 3) is a local minimum.

D=12 and f(1, 3) is a local maximum.

D=0 and the Second Derivative Test gives no information about f(1, 3).

D=3 and f(1, 3) is a local maximum.

D=-30 and f(1, 3) is a saddle point.

1.

D=3 and f(1, 3) is a local minimum.

2.

D=12 and f(1, 3) is a local maximum.

3.

D=0 and the Second Derivative Test gives no information about f(1, 3).

4.

D=3 and f(1, 3) is a local maximum.

5.

D=-30 and f(1, 3) is a saddle point.

Explanation / Answer

D = fxx*fyy - (fxy)^2

D = (-2)(-6) - (-3)^2

D = 12 - 9

D = 3

D > 0 and fxx < 0

So, the point is a LOCAL MAXIMUM

Option 4