Thread: How do I find the work required to move an object in the force field?

Find the work required to move an object in the following force fields along a straight line between the given points. Also is the Force conservative?

F=<x,y> from A(1,1) to B(3,-6)

My book doesn't cover this real well. Please show your work. Thank you.

F has potential f defined by f(x,y) = (x² + y²)/2 (i.e. ?f = F),
so F is conservative and the work done is independent of path.
The work done from A to B is then
f(3,-6) - f(1,1) = 43/2.