1. Find the directional derivative of f(x, y, z) = x + 2y - 322 at the point Po(2, -1, 1) in the direction of the vector 27 - 23 + k. (Start by computing the gradient Vf(x, y, z) and don't forget to make the direction unit.) 2. For f(x, y) = In(x2 + y?) and the point (2, 2), find the gradient at the point and sketch the gradient together with the level curve that passes through the point. (Repeat with points (2, -2), (-2, 2), and (-2, -2).) What do you observe? (Hint: For the level curve, start by computing f(2, 2) and then figuring out what the level curve In(x2 + 32) = f(2, 2) looks like. You can also confirm using Mathematica's ContourPlot [. . .].) 3. For h(x, y, z) = In(x2 + y2 - 1) + y + 6z and the point Po(1, 1, 0), find the directions in which h increases and decreases most rapidly at Po. Then determine the directional derivatives of h in these directions. 4. In what direction(s) is the directional derivative of f(x, y) = xy + x2 at P(2, 3) equal to 0