Which of the following best describes the function f(x, y) = 2x3 - 3x2 - y2 at t

Question

Which of the following best describes the function f(x, y) = 2x3 - 3x2 - y2 at the point (0,0)? Local maximum Local minimum Saddle point It is a stationary point but the 2nd partials test is inconclusive It is not a stationary point Which of the following best describes the function f(x, y) = 2x3 - 3x2 - y2 at the point (-1,0)? Local maximum Local minimum Saddle point It is a stationary point but the 2nd partials test is inconclusive It is not a stationary point Which of the following best describes the function f(x, y) = 2x3 - 3x2 - y2 at the point (1,0)? Local maximum Local minimum Saddle point It is a stationary point but the 2nd partials test is inconclusive It is not a stationary point

Explanation / Answer

8) Fx =6x^2 - 6x , r = Fxx = 12x -6 ,s =Fxy = o

Fxx at (0,0) = -6 <0

Fy = -2y , t =Fyy = -2

[rt - s^2 ] > 0 and [r] <0 then F(x,y) is local maximum

Here

-6 * -2 - 0 = 12 > 0 and r =-6 < 0

option A

9) Fx =6x^2 - 6x , r = Fxx = 12x -6 ,s =Fxy = o

Fxx at (-1, 0) = -12-6 =-18 <0

[rt - s^2 ] > 0 and [r] <0 then F(x,y) is local maximum

-18 * -2 -0 = 36>0

option A

10) Fx =6x^2 - 6x , r = Fxx = 12x -6 ,s =Fxy = o

Fxx at (1, 0) = 12-6 = 6

[rt - s^2 ] < 0 then F(x,y) is neither maximum nor local minimum. (1,0) is called Saddle point

Here

12 * -2 - 0 =-24 <0

option C

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