2. Find if y 2 - 3xy + x 2 = 7.

3. Find for 2x 2 + xy + 3y 2 = 0.

4. Find if xy 2 - y = x 2. Find if xy 2 - y = x 2.

5. Find if y = sin(x + y).

6. Find if x = tan(x + y).

7. Find in terms of x and y: y 3 - xy = 5

8. Find then evaluate the derivative at the point (0, 2): x 2 - 2xy = y 2 - 4.

9. Find then evaluate the derivative at the point (0, 2): x 2 - 2xy 2 = y 3 - 8.

10. Find then evaluate the derivative at the point (0, 0): 2x - 5x 3 y 2 + 4y = 0.

11. Find then evaluate the derivative at the point (1, -1): x 4 + 4x 2 y 3 + y 2 = 2y.

12. Find then evaluate the derivative at the point (0, -2): x 2 - y 2 - 2x - 4y - 4 = 0 undefined

13. Determine the slope of the graph of 2x 2 - 3xy + y 3 = -1 at the point (2, -3).

14. Find the slope of the line tangent to the graph of 4y 2 - xy = 3 at the point (-1, -1)

15. Find the slope of the line tangent to the graph of 4y 2 - xy = 3 at the point

16. Find the point(s) (if any) of horizontal tangent lines: x 2 + xy + y 2 = 6. and

17. Find an equation of the tangent line to the graph of x 2 + 2y 2 = 3 at the point (1, 1) x + 2y = 3

18. Find an equation of the line tangent to the curve x 2 + y 2 = 9 at the point (3, 0) x = 3

19. Find an equation of the line tangent to the curve 2y 2 - x 2 = 1 at the point (7, -5)

20. A machine is rolling a metal cylinder under pressure. The radius of the cylinder is decreasing at a constant rate of 0.05 inches per second and the volume V is 128π cubic inches. At what rate is the length h changing when the radius r is 1.8 inches? [Hint: V = pr 2 h] 2.195 in./sec

21. As a balloon in the shape of a sphere is being blown up, the volume is increasing at the rate of 4 cubic inches per second. At what rate is the radius increasing when the radius is 1 inch? in./sec

22. Sand is falling off a conveyor onto a conical pile at the rate of 15 cubic feet per minute. The diameter of the base of the cone is approximately twice the altitude. At what rate is the height of the pile changing when it is 10 feet high? 0.048 ft/min

23. A point moves along the curve y = 2x 2 + 1 in such a way that the y value is decreasing at the rate of 2 units per second. At what rate is x changing when Decreasing unit/sec

24. The formula for the volume of a tank is V = πr 3 where r is the radius of the tank. If water is flowing in at the rate of 15 cubic feet per minute, find the rate at which the radius is changing when the radius is 3 feet. ft. / min

25. Air is being pumped into a spherical balloon at a rate of 28 cubic feet per minute. At what rate is the radius changing when the radius is 3 feet? ft./min

26. Two boats leave the same port at the same time with one boat traveling north at 35 knots per hour and the other boat traveling east at 40 knots per hour. How fast is the distance between the two boats changing after 2 hours? 53.2 knots/hr

27. The radius of a circle is increasing at the rate of 2 feet per minute. Find the rate at which the area is increasing when the radius is 7 feet. 28π ft 2 /min

28. A 5-meter-long ladder is leaning against the side of a house. The foot of the ladder is pulled away from the house at a rate of 0.4 m/sec. Determine how fast the top of the ladder is descending when the foot of the ladder is 3 meters from the house. -0.3 m/sec

29. A metal cube contracts when it is cooled. If the edge of the cube is decreasing at a rate of 0.2 cm/hr, how fast is the volume changing when the edge is 60 centimeters? -36.0 cm 3 /hr