Question

Determine whether or not F is a conservative vector field.  If it is, find a function f  such that

Answer 1

Step 1:

The function is .

Definition of conservative :

In a vector field , if then F is conservative.

The function is .

Here .

So F is conservative.

Step 2:

Find the potential function for .

To find the potential function, follow the condition .

         equation  (1) 

          equation  (2) 

From equation  (1)  and equation (2),  .

Solution :

F is conservative.

The potential function is .