II. Application/Analysis (Technology allowed, show ALL work!) 1. Let f(x, y) = 3x2 + 4y2 be a given surface. a) Find the equation of the tangent plane at (2, 1, 16), with final answer in standard form (5 points). b) Compute Duf (2, 1), the directional derivative, where u is the unit vector pointing in the direction 0 = 120. (4 points). 2. Let f (x) = - x4. 16 - -x2. Find the equation of the osculating circle to the given function at the origin. (5 points)3. Use spherical coordinates (be careful on this problem) to evaluate the following triple integral (6 points): 2 \"WI-y: 1t4-3'72-3": f f f xix? + y? + z2 dzdxdy -2 U ~./4x2y2 4. Using either the Hessian method of optimization or the method of Lagrange multipliers (your choice), find the points on the surface y2 = 9 + xz that are closest to the origin. (5 points)