Find the critical points if any, local max, local min, saddle points if any of t

Question

Find the critical points if any, local max, local min, saddle points if any of the following function. Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, local minimum, or saddle point.

f (x,y) = 2x^2 - 3y^2 + 1

Critical points? =

Local Max? =

Local Min? =

Saddle Points?

Please answer as I have described in order. Last person did not and I lost a question. If you do not know how to do this problem please do not attempt it. Thank you!

Explanation / Answer

f (x,y) = 2x^2 - 3y^2 + 1

fx=0==>4x=0==>x=0

fy=0==>-6y=0==>y=0

(0,0) is critical point

fx=4x==>fxy=0

fx=4x==>fxx=4

fy=-6y==>fyy=-6

D=(fxx fyy)-(fxy)^2 =(4* -6)-0^2 =-24<0

==>(x,y)=(0,0) is the saddle point

no

Local Max

Local Min

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