Question

Determine if the vector field is conservative and find the respective function if it is:

a) Yes, f(x)
b) No, undefined
c) Yes, g(x)
d) No, constant

Answer 1

To determine if a vector field is conservative, we need to check if the derivatives of the components of the force satisfy a certain condition.

Step-by-step explanation:

To determine if a vector field is conservative, we need to check if the derivatives of the components of the force satisfy the condition (dFy/dx) = (dFx/dy). If the condition is satisfied, then the vector field is conservative. Let's go through each option:

a) Yes, f(x): Since f(x) is not defined, this option is incorrect.

b) No, undefined: This option is correct as the vector field is not conservative.

c) Yes, g(x): Since g(x) is defined, this option is incorrect.

d) No, constant: This option is incorrect as a constant vector field is always conservative.