Answer questions in detail

Problem 1 Let f(x, y) = 12 - ry + y' -y. Find the direction u and the values of Duf (1, -1) for which Duf(1, -1) =0 Problem 2 Let sin(E-W) f(1, y) = Ixl + lyl # 0 (x, y) = (0,0) Is f continues at the origin? Why? Problem 3 Find T, N, B. k as functions of t if r(t) = (sint)i + (v2cost)j + (sint)k. Problem 4 Find dw/dt at t = 1 if w = re" + ysing - cosz, = = 2vt, y = t - 1 and z = nt. Problem 5 Find all the local maxima, local minima, and saddle points of the functions f(x, y) = 2ry - x2 - 2y' + 3x +4 Problem 6 Find equations for the tangent plane and normal line at the point Po on the given surface a2 + 2ry - y + 22 = 7, Po(1, -1,3). Problem 7 Show that (0, 0) is a critical point of f(x, y) = 12 + kry + y? no matter what value the constant & has. (Hint: Consider two cases: k = 0 and k # 0.)