Let be a function . And let be a critical point of and the Hessian of this function at point .

Check the incorrect answer .

Question

Let    be a function   . And let    be a critical point of    and    the Hessian of this function at point   . 
 
 Check the  incorrect answer .

Answer

If   ,    is positive semi-definite, then    is convex in    and    is a global minimum.

Answer

If   ,    is positive-definite, then    is strictly convex in    and    is the only global minimum.

Answer

If    is a local maximum, then    is negative-definite .

Answer

If   ,    is negative semi-definite, then    is concave in    and    is a global maximum.

Answer

If    is positive-definite, then    is a local minimum.

Answer

If   ,    is negative-definite, then    is strictly concave in    and    is the only global maximum.

Answer

If    is nor semi-negative-definite, nor positive semi-definite and   , then    is a saddle point.

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