find the equation of the plane tangent to the given level surface at the point corresponding to x = 0 and y = -1. 9. Let f(x, y) = 2-24+2x2 -y2. Determine if each of its critical points is a relative minimum, relative maximum, or saddle point. 10. Find the absolute maximum and minimum values of f (x, y) = 23 - 3x - y3 + 12y on the set R which is the region enclosed by the quadrilateral whose vertices are (- 2, 3), (2, 3), (2, 2), and (-2, -2). 11. Use two different techniques to find the points on the cone z2 = x2 + y that are closest to the point (4, 2, 0).2. Let f(x, y, z) = exy-z. Find fryz. 3. The plane y + z - 3 intersects the cylinder x2 + y = 5 in an ellipse. Find the line tangent to the ellipse at the point (1, 2, 1). 4. The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by x = V1 + t, y = 2 + ;t, where x and y are measured in centimeters. The temperature function satisfies Tx(2, 3) = 4 and Ty(2, 3) = 3. How fast is the temperature rising on the bug's path after 3 seconds? 5. One side of a triangle is increasing at a rate of 3 cm/s and a second side is decreasing at a rate of 2 cm/s. If the area of the triangle remains constant, at what rate does the angle between the sides change with respect to time when the first side is 20 cm long, the second is 30 cm long, and the angle is ". (The area A of a triangle with sides of lengths x and y with an angle of 0 between them is given by A = y sin(0). Assume that for a fixed area A the equation A - Ty sin(0) defines 0 implicitly as a function of x and y.) 6. Find the directions in which the directional derivative of f(x, y) = x2 + xy at the point (2, 1) has the value 2. 7. Let f be a function of two variables that has continuous partial derivatives and consider the points A(1, 3), B(3, 3), C(1, 7), and D(6, 15). The directional deriva- tive of f at A in the direction of the vector AB is 3 and the directional derivative at A in the direction of AC is 26. Find the directional derivative of f at A in the direction of the vector AD. 8. Assume that the level surface equation x' ty + 28 + 6xyz - 1 defines z implicitly as a function of r and y. Find zx(0, -1) and zy (0, -1). Use that information to