This problem is about the function

f(x,y,z,w)=acosx+acosy+acosz+acosw+xy+yz+zw

which is a function of four variables, and it has a critical point at x=y=z=w=0x=y=z=w=0 (this is obvious; you do not need to verify it).

A. Classify the critical point, assuming a=0.

B. Classify the critical point, assuming a=1/2.

C. Classify the critical point, assuming a=1.

D. Classify the critical point, assuming a=.

E. Classify the critical point, assuming a=2.

F. Determine the values of a for which the second derivative test fails, at the given critical point.

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