Problem 1. Let w(x, y) : yer 7 $32 a) Compute the gradient V11) at the point (1, 1). b) Compute the directional derivative D<_171>w(1, 1). c) Find a vector u such that the directional derivative Duw(1, 1) equals zero. d) Estimate the value of w at (0.9, 0.9). Problem 2. Consider the function f(x, 1/, 2) = sin(xy2). (a) Compute the gradient Vf(7r,0, W/Q). (1)) Compute the directional derivative Duf(7r, 07 7T/2) for the vector u = (, 0, f; (c) Find all the directions u for which the directional derivative Duw7 0, 7r/2) is zero. (d) What are the directions 11 for which the above directional derivative reaches its maximum? minimum? Problem 3. You are climbing the mountain z = 100 41:2 22/2 and you are in the point (1, 3, 81). In which direction (in 2D with a: and y coordi nates) should you move if you want to reach the summit as soon as possible? Problem 4. True of False? Please motivate your answer. Let u be any nonzero vector and let x, 9) = sin(x) + sin(y). Then \\/ S Bufng) S @