T2 Problem 1. Let w(:r, y) 2 ye? 7. a) Compute the gradient Vw at the point (1,1). b) Compute the directional derivative D w(1,

T2 Problem 1. Let w(:r, y) 2 ye"? 7. a) Compute the gradient Vw at the point (1,1). b) Compute the directional derivative D<_1>w(1, 1). c) Find a vector 11 such that the directional derivative Duw(l,1) equals zero. (1) Estimate the value of to at (0.9, 0.9). Problem 2. Consider the function ag/51.2) = sin($yz). (a) Compute the gradient Vf(7T, 0, 7T/2). (b) Compute the directional derivative Duf(7T, 0, 7T/2) for the vector u = ($3 0: )- (0) Find all the directions 11 for which the directional derivative Duf(7r, 0, 7r/2) is zero. (d) What are the directions u for which the above directional derivative reaches its maximum? minimum? Problem 3. You are climbing the mountain 2 : 100 $2 23,12 and you are in the point (13,81). 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 non-zero vector and let f(:l:,y) = sin(a:) + sin(y). Then \\/ 3 Dufmy) S x/i