# What is a saddle point?

Jun 30, 2015

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

#### Explanation:

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]}