Show all your work. This is an opportunity to practice communicating your mathematical reasoning in a clear and concise manner. 1. Consider the vector field F(x, y) = (1 + 4)i -2xj (a) Is the vector field a gradient vector field? If so, find a suitable f(z, y) such that Vf = F. If not, explain briefly why not. (b) Is the vector field path-independent (also called conservative)? (Yes or No) (c) Compute the curl of F