If fx(a,b)=fy(a,b)=0, does it follow that ƒ has a local maximum or local minimum at (a, b)?

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tabuordy · Accepted Answer

Step 1  To determine:  Whether the function f follows that it has a local maximum or local minimum at a point (a, b) if the following condition is given  fx(a,b)=fy(a,b)=0  Step 2  Explanation:  Let the given function z=f(x, y)  By using the definition of the saddle points of the function,  The point (x1,y1)  is a saddle point of the function f(x, y) if both the partial derivatives fx(x1,y1)=fy(x1,y1)=0  but f has no local maximum or local minimum at (x1,y1).  Here the given condition is fx(a,b)=fy(a,b)=0  So, the point (a, b) is the saddle point of the function f(x, y)  Therefore, the function f  does not have a local maximum or local minimum at a point (a, b).

If f_{x}(a, b) = f_{y}(a, b) = 0, does it follow that ƒ has a local maximu

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