Q. 4 - Calculus

Question

What is a stationary point of a function of two variables, f(x, y)? What, if anything, is the difference between a critical point and a stationary point of f ? 

Step-by-Step Solution

Answer

For a function of two variable(x) the stationary point is a point in the domain of f(x ,y ) at which the function is differentiable and the gradient of the function vanishes, that is $\nabla f( x , y ) =0$

Step 1. Given

A function of two variables, f(x, y) 

Step 2. Stationary point .

For a function of two variable(x) the stationary point is a point in the domain of f(x ,y ) at which the function is differentiable and the gradient of the function vanishes, that is $\nabla f( x , y ) =0$

A critical point is not the same as the stationary point, as at the critical point a function may of may not be differentiable that is $\nabla f( x , y )$ may not exists at a critical point. Every stationary point is a critical point but the converse is not true