Math& 163 Spring 2023 "Differentiation of Functions of Several Variables" Challenge Set INSTRUCTIONS: Please do your work on a separate sheet or sheets of paper. To receive full credit, a problem must be solved correctly and completely, with all relevant work shown; solutions should be clear, concise, and thorough. Use complete sentences as appropriate. Sloppy or incomplete work will not receive full credit, even if the solution is correct. You are strongly encouraged to make use of rough drafts before writing up your final submission. 1. Given the function z = 2-3y?+22 6 2xty-42 , find the point on the graph where a and y both equal (3) 1. In other words, find the value of n for the point (1, 1, n) for this function. Describe any difficulties you had finding this value. Describe what you did to overcome those difficulties. 2. Given the same function z = 2, By , find the equation of the plane tangent to the (8) surface of the function at the point you found in the first part of this question. 3. Given the same function z = 2 3 , find and maximize the directional derivative of (7) this function from the point you found in the first part of this question. 4. Given the same function z = -342+22 2rty-42 , determine and describe (classify) the critical (8) points for this function over the rectangle (-2, 2) x (-2, 2). Math& 163 "Differentiation of Functions of Several Variables" Challenge SetEND OF SET]