Understanding Saddle Points in Partial Differentiation - Explained with Examples

[ZedCar]

I'm working through a partial differentiation problem, to which I have the answer.

The function being 4x^2+4xy-y^3-2x+2 to which the stationary points must be obtained and classified.

At the end of the working out, when partial differentiation is conducted and a number of -32 is obtained, it states that because this is a negative number this is a "saddle point". Is this another term for a "point of inflection"?

How can they make this claim? I thought since the number obtained is negative it would therefore be a maximum turning point.

The second number obtained with the second partial differentiation is 32, and it states since this is a positive number this is a minimum turning point; which I understand.

Thank you.

 

[jedishrfu]

saddle points http://en.wikipedia.org/wiki/Saddle_point

and points of inflection http://en.wikipedia.org/wiki/Point_of_inflection

in the categorization section yes saddle point is a point of inflection

 

[LCKurtz]

I'm working through a partial differentiation problem, to which I have the answer.

The function being 4x^2+4xy-y^3-2x+2 to which the stationary points must be obtained and classified.

At the end of the working out, when partial differentiation is conducted and a number of -32 is obtained, it states that because this is a negative number this is a "saddle point". Is this another term for a "point of inflection"?

Just to add to the other reply. For a function of one variable a saddle point is a point of inflection, but an inflection point need not be a saddle point since the slope need not be zero.

For a function of two variables a saddle point is a stationary point that is neither a max nor a min point. The term "inflection point" is not used for functions of two variables that I know of.

 

[ZedCar]

Thanks very much for the info guys!. Much appreciated, Thank you.