Q 5 - Calculus

Question

What is a saddle point of a function of two variables, $f\left(x,y\right)$?

Step-by-Step Solution

Answer

Saddle points of a two variable function :-

A critical point of a two variable function $f(x,y)$ is saddle point which is neither local maxima nor local minima.

Step 1. Given Information

We have to define that what are the saddle points of a two variable function $f\left(x,y\right)$.

Step 2. Define saddle points

We have a two variable function $f\left(x,y\right)$.

We classify the critical points of two variable function in three types :-

• Local Maxima
• Local Minima
• Saddle points

Here we have to define saddle points.

Saddle point is a critical point of a two variable function with one condition.

We know that a critical point is a point which may be local maxima or local minima.

But there exists critical points of a two variable function which is neither local maxima nor local minima. These type of critical points are called saddle points.

In short we can say that :-

A critical point of a two variable function $f\left(x,y\right)$ is saddle point which is neither local maxima nor local minima.