What is a saddle point?

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Answer 1 · 2015-06-30T18:46:01

Coming from one direction it looks like we've hit a maximum, but from another direction is looks like we've hit a minimum.

Here are 3 graphs:

$y = x^4$ has a minimum at $x=0$

graph{y = x^4 [-12.35, 12.96, -6.58, 6.08]}

$y = -x^2$ has a maximum at $x=0$

graph{-x^2 [-12.35, 12.96, -6.58, 6.08]}

$y = x^3$ has a saddle point at $x=0$

graph{x^3 [-12.35, 12.96, -6.58, 6.08]}

Coming from the left it looks like a maximum, but coming from the right it looks like a minimum.

Here's one more for comparison:

$y=-x^5$

graph{-x^5 [-10.94, 11.56, -5.335, 5.92]}