3. Consider the function f(x, y) = y' cos(x) on the domain {(I, y) ( R'| - 2n

3. Consider the function on the domain { (x, y) R21 2m x S 2m, Below is a plot of f on this domain. 30 20 10 -10 -20 -30 4 2 -2 = ya cos(x) 5 (a) Find an expression for the gradient vector of f and evaluate it at the point , 2 that is x 6 (b) Compute the directional derivative Duf , 2 at the point and in the direction 6 (c) (d) of the vector (2, 1). Find all critical points in the given domain. Find the value of f at these critical points. Apply the Two-Variable Second Derivative Test to these critical points, and interpret the outcome. Show all working. Is measured in degrees or radians? Justify your answer.