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Thread 'How to Find Critical Points of function f(x,y,z)'

Hi everybody If we have not any answers for critical points after first partial derivatives equal to zero, how can we continue to find local MAX, local MIN and Saddle point?. For example: Suppose we have below equations for first partial derivatives: ∂ƒ/∂x = y + 5 , ∂ƒ/∂y = 2z , ∂ƒ/∂z = y As you can see, for ∇ƒ= 0 , there are not any answers (undefined)

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