Suppose that a function f(x,y) has a critical point (a, b) at an interior point in its domain and that f has continuous second order partials in a neighbourhood of (a, b).
If , then f has no local extremum at (a, b).

Question

Suppose that a function f(x,y) has a critical point  (a, b) at an interior point in its domain and that f has continuous second order partials in a neighbourhood of (a, b).
If     , then f has no local extremum at (a, b).

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The Answer of Suppose that a function f(x,y) has a critical point  (a, b) at an interior point in its domain and that f has continuous second order partials in a neighbourhood of (a, b).
If     , then f has no local extremum at (a, b).

Suppose That a Function F(x,y) Has a Critical Point