Please answer these questions with explanation

5. Find and classify the critical points of f (x, y) = 2x + xy2+ 5x2 + y2.6. Consider the vector field F : R3 -> R3 defined by F(x, y, z) = (x - y, - 2xy, z). a) Show that F is a gradient field by verifying that curl (F) = (0,0, 0). b) Find a function f : R' -> R such that Vf (x, y, z) = F(x, y, z). c) Compute F.dr where C is a curve with the initial point (1, 0, -1) and the terminal point (2, 1, 0)