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Chapter 12: Q. 4 (page 974)

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 ?

Short Answer

Expert verified

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∇f(x,y)=0

Step by step solution

01

Step 1. Given 

A function of two variables, f(x, y)

02

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 ∇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 ∇f(x,y)may not exists at a critical point. Every stationary point is a critical point but the converse is not true

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