-X 4. Given U = ete* - and V= e* - e 2 2 -, show that U' + v' = ex [10] 5. Show that the function y = 5 1 - cos 10 has a horizontal tangent when X = 20x [10 ] THINKING AND INQUIRY [40]: 6. Determine the values of a, b, c if the function f(x) = ax + bx + c passes through the point (2, 19) and has a horizontal tangent at ( -1, 8). [10] 7. On an island located in the North, the winter temperature on some days can be predicted using the function C = -40 +6sin (t-10) , where t is the number of hours since midnight, and C is the temperature in degrees Celsius. Find the instantaneous rate of change of the temperature at 4:00 a.m. AND interpret your result. [10] 8. Determine equation of the tangent to the curve f (x) = -5x (3x-4)2 at x = 1. [10] 9. A small body with a temperature of 50"C is placed in a room with air temperature 20"C. The formula below is used to predict the temperature, C, of the body t minutes later: C=30e-0.02037 + 20 Find the instantaneous rate of change in the temperature of the body at the time when it has cooled to 45 C . [10]