Answer questions 1-32

True/False Indicate whether the statement is true or false. 1. The quotient rule can be used to differentiate a rational function. 2. The slope of a tangent to a curve is found by equating the derivative to the x-coordinate of the tangent point. 3. The first derivative test is used to find points of inflection. 4. A rational function always has a vertical asymptote. 5. The constant multiple, sum, and difference differentiation rules do not apply to sinusoidal functions. 6. There are an infinite number of tangents with a given non-zero slope to a sinusoidal curve. 7. If a sinusoidal function is not even, then its derivative is even. 8. The inverse of an exponential function is a logarithmic function. 9. Another way of expressing Inx is log x. 10. The decay of a radioactive substance can be represented by more than one exponential model. Multiple Choice Identify the choice that best completes the statement or answers the question. 11. Evaluate the limit, if it exists: lim 25-x2 x-5 a. 10 C. 0 b. -10 d. does not exist12. Evaluate the limit for the graph: lim f(x). 4 2 -4 -2 0 4 -4 a. 0 C. 2 b. -1 d. does not exist 13. Find f NI- if f(x) = 2 a. 8 C. - N b. -8 d. 14. Determine the equation of the tangent to the graph of y = (x] -3 ) at the point (-2, 1). a. y = -8x - 15 C. V= -8x +8 b. y = 8x + 15 d. y=-2x-315. When does the function /(x) = x (x -1) have a local maximum? a. (1, 0) C. (-1, 0) b. (0. 0) d. (-1, 1 ) 16. Determine the number of local extrema for the graph of /(x). y 1.0 0..5 -10 -05 0 -0.6 a. 4 1.17. Find the critical points for the function /(x) = 12x-x]. a. (2, 16) and (-2, -16) c. (2, -16) and (0, 0) b. (0. 0) and (1, 2) d. (2, 16) and (1, 11) 18. Find the slope of the tangent to the curve y = cos x - sin x atx = 4 -2 C. b. d. 19. Ify = sin x, find y" atx = 0. 1 C. d. 20. Ify =- COS 2x 4 `, find y" atx = 1. a. 1 C. b. 0 d. 2 21. Find the slope of the tangent to y = cos x - sin x at the point where x = = 4 1 c. 2 b. d. -1 22. If /(x) = , find f '(-1). C. d. 23. If Ax) =(x - le , find / (1). a. 2 C- b. d.Short Answer 24. Determine the average rate of change of /(x) = = 1 -x - over the interval 2 S x $ 3. 25. Use the first principles definition of the derivative to find / '(2) where ((@) = Name: ID: A 26. The position function of a object thrown on the moon is given by s(() =6.5-0.83/, where time, r, is in seconds and distance, s, is in metres. Find the maximum height of the object. 27. The cost function for producing x units of a product is C(x) = -0.003x +4.2x + 3000. The revenue function is R(x) = 138x -0.15x. Determine the marginal profit for the sale of 100 units of the product. 28. Find the equation of the tangent to the curve Ax)= x-, (3x + 5x] ] at the point (1, 4). 29. Find the equation of the tangent to the curve y = 2sinx + sin x at the point where x =30. The horizontal position of the pendulum of a grandfather clock can be modelled by M(() = A cos 2nt T , where A is the amplitude of the pendulum, / is time, in seconds, and 7 is the period of the pendulum. Determine the formula for the velocity of the pendulum at time f. Problem 31. Determine the equation of the tangent to /(x) = 3r + 5x + 2 at the point (1, 10). 32. In a ski resort town, the number of people employed, p(), during any given month, f, can be modelled by the function p(/) = 2300sin # ( + 1)|+ (#+ 1) |+5500, where I s/ $ 12 and / = 1 represents January, / = 2 represents February, etc. Determine the maximum and minimum number of people employed during the year and in which month they occur