All multiple-choice questions

Multiple Choice: Circle the correct answer. 1. Evaluate lim f ( 4 + h) - f(4) h -0 h , where f (x) = Vx . a. C. b. OO d. 4 2. Let f(x) = 5x*+ 3x + 2. Determine f '(x). a. 10x + 3 7x + 3 b . 10x + 5 d . 7x + 5 3. What is the slope of the tangent line to the graph of the function (x) = x - 3x at the point (2, 2)? a. 9 C. b. -9 d. 4. The position in metres of a particle at time t in seconds is d(!) = 31- 17, where 2 0. Find the acceleration of the particle when t = 4. a. 124 m/s C. 127 mis b. 19 m/s d. 72 mis-5. For the function f(x) = x - 3x + 1, state the intervals on which the function is increasing. a. x 1 x > -1 and x -1 and x > 1 6. The possible point of inflection of f(x) = x - - x 3 is : 32 A I W a. 31 3 ' 27 c . 4 32 b. d . 3 32 27 4' 27 7. Which of the conditions listed below best characterizes the given graph of f(x)? do a. lim f(x) exists, f(-2) exists, lim f(x) = f(-2) * - -2 2 - + x b. lim f(x) does not exist, f(-2) does not exist * - -2 C. lim f(x) does not exist, f(-2) exists X- -2 d. lim f(x) exists, f(-2) exists, lim f(x) = f(-2) * - - 2 * +-28. What is the derivative of f(x) = x- 1 x + 3 a. f' (x) = 1 4 C . f' ( x) = (x+ 3 )- 4 b. f' ( x) = 2 d. f' (x) = x +9 (x+ 3)2 9. Differentiate y = V4x - 9 2 a. V4x -9 C. 4(4x - 9)2 b. 2V4x-9 d. -V4x-9 3 10. Let f(x) = (2x - 3) Determine the equation of the tangent to the curve at (1, 3). a. 6x-y - 3 =0 3x - y = 0 b . 3x - 4y+9 =0 12x-y- 9 =0 11. If y = xet, then dy is : dx a. C. er b. ex+ xet x- tex12. The slope of the tangent to the curve y = ex at x = 0 is: a. O C . -1 b. - d