Saddle point and inflection point are two things I have a hard time differentiating! They are not the same, graphically, but what are the key mathematical differences between them both?

Without looking at the graph, how would you be able to tell, just by doing certain computations to the formula, whether or not it's a saddle point? And that comes down to something called the second …

Once you find a point where the gradient of a multivariable function is the zero vector, meaning the tangent plane of the graph is flat at this point, the second partial derivative test is a way to tell if that …

Will it be a saddle point if the second partial derivative of x and the second partial derivative of y have different signs? As in one is positive and the other is negative? If this is the case then we probably …

Well, mathematicians thought so, and they had one of those rare moments of deciding on a good name for something: Saddle points. By definition, these are stable points where the function has a local …

This is not a question, but for anyone a little confused as to why the quadratic form being negative and positive at times corresponds to a saddle point, I think I have the answer.

For the graph of an exponential function, the value of y will always grow to positive or negative infinity on one end and approach, but not reach, a horizontal line on the other. The horizontal line that the …

But when we look at the graph this isn't true, it's not a local minimum, it's a saddle point. So what this tells us is that these two second partial derivatives aren't enough, we need more information.

It was thorough in making students understand the purpose of second-order partial derivative, saddle point, positive concavity, negative concavity and local maxima and minima.

However, in multivar calculus there is something really annoying called the "saddle point." Though it is not a local extremum, it does provide an opportunity for the graph (or value) to "turn around," since it …