in depth explanation

.; 1'; [HI-1': 2.5 _________-\" 1 1. The graph of f is shown below. 12. 13. Chapter 2 - The Derivative Function ' 117 a) Where does f have critical numbers? b) On what intervals is f ' negative? c) On what intervals is f ' increasing? (1) Where does f' achieve its maximum value? Estimate this value of f '. 6) Sketch a graph of f '. The graph of g is shown below. a) Where does g have critical numbers? b) On what intervals is 3' negative? Positive? c) On what intervals is g' increasing? Decreasing? d) Sketch a graph of g' . The slope of a curve at any point (x, y) is given by g = (x 2.)2 (x 3). Determine Whether the following statements are true or false. a) The curve has a horizontal tangent at the point where x = 2. b) The curve has a local minimum at the point where x = 2. c) The curve has a local maximum at the point where x = 3. d) The curve is increasing at x = 2. 118 Chapter 2 - The Derivative Function 2.5 14. The graph of the derivative of a function f is shown below. up; u... -c. is\": a) On which intervals is f increasing? Decreasing? b) Where does f have critical numbers? ! c) Where does f have a local maximum? A local minimum? I d) Suppose f (0) = 0. Sketch a possible graph of f . 15. The graph of the derivative of a function g is shown below. " 3 ' i I a) On which intervals is 3 increasing? Decreasing? b) Where does g have critical points? I d) Suppose 3(0) = 1. Sketch a possible graph of g. I 1.6. Suppose the derivative of a function y = f (x) is Q = x + 3. ' l c) Where does g have a local maximum? A local minimum? l .. - ' a) On what intervals, if any, is f increasing? b) At which x, if any, does f have a local minimum? 0) Suppose f (2,) = 1. Sketch a possible graph of f. ' 17. Let f (x) = ecosx' How many zeros does f' have in the interval [0, 211:] ? I Where are they located? i