Answer Happy

A This question has several parts that must be completed sequentially. If you sko a part of the question, you will be able to come back to the apped part Tutorial Exerci Find the maximum rate of change of fat the given point and the direction in which it occurs Rx, y)=sin(x), (2.0) Step 1 Recall that the direction in which the maximum rate of change of fx, y) occurs at a point (a 5RX,Y)= con (ry),ros (y)) Step 2 Therefore, at the point (2, 0), the direction of maximum rate of change is the vector 02.0) (0 (0), 2-cas(0) The maximum rate of change is given by ta which is 101201-[ az əs B) Use the Chain Rule to find the indicated partial derivatives. z = x¹ + x²y, дz дz дz as at du F əz at az ди 11 9,(0,0)= 9,(0,0) = P) 11 11 points for the shipped part, and you wil net x = s + 2t - u, y = stu²; when s = 2, t = 1, u = 5 Suppose f is a differentiable function of x and y, and g(u, v) = f(e" + sin(v), e cos(v)). Use the table of values to calculate (0, 0) and g(0,0). fx fy 1 0 3 6 0 1 5 8 (0, 0) (1, 2) Find the directional derivative of f at the given point in the direction indicated by the angle 8. f(x, y) = y cos(xy), (0, 1), 0 = 1/3