1. For ,f(x,y, z)=x'+y?+23+6n:-1 where z is a function ofx and y: z=x2+),2 . Butxandy are not a function of anything else. Construct a tree diagram to find-and-. cry f(x,y,z)=(xy: .Find the directional derivative D f at the point (2,4,2) in the direction of the vector 2. For (4,2,-4) (Caution: this is NOT a unit vector) Find the gradient vector Vf at the point (2,4,2) Use your findings to confirm that Vf.u = D, · Aplate is heated and the temperature distribution profile Tis found to follow T(x,y,z)=200eã - +/ 3. a. Find the temperature change when you move from the point A(2,, 2) to the point B(3,-3, 3) b. In what direction at the point A(2,-1, 2) will you experience the greatest temperature change? (In practive, you would have to find the 3 direction cosines, but for the purpose of this exercise, you can simply find the vector) 4. Use the second partial derivative test to determine the maximum and minimum points, if any, for f(x,y) = x,y + 12r'-8). If the test reveals any saddle point, be sure to indicate it as well