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
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