University:
Whitman College
Course:
MATH-125 | Calculus I
Academic year:

2021
Views:

433

Pages:

1
Author:

Alexa Maynard

164 |||| CHAPTER 2 LIMITS AND DERIVATIVES 35–38 The graph of f is given. State, with reasons, the numbers at which f is not differentiable. 36. y 35. 43. The ﬁgure shows the graphs of three functions. One is the position function of a car, one is the velocity of the car, and one is its acceleration. Identify each curve, and explain your choices. y y a 0 _2 37. 0 x 2 0 4 x 4 x b c t 0 38. y _2 2 y 0 _2 2 x 44. The ﬁgure shows the graphs of four functions. One is the ; 39. Graph the function f ͑x͒ ෇ x ϩ sԽ x Խ . Zoom in repeatedly, ﬁrst toward the point (Ϫ1, 0) and then toward the origin. What is different about the behavior of f in the vicinity of these two points? What do you conclude about the differentiability of f ? position function of a car, one is the velocity of the car, one is its acceleration, and one is its jerk. Identify each curve, and explain your choices. y d a b c ; 40. Zoom in toward the points (1, 0), (0, 1), and (Ϫ1, 0) on the graph of the function t͑x͒ ෇ ͑x 2 Ϫ 1͒2͞3. What do you notice? Account for what you see in terms of the differentiability of t. 0 t 41. The ﬁgure shows the graphs of f , f Ј, and f Љ. Identify each curve, and explain your choices. y ; 45– 46 Use the deﬁnition of a derivative to ﬁnd f Ј͑x͒ and f Љ͑x͒. Then graph f , f Ј, and f Љ on a common screen and check to see if your answers are reasonable. a 45. f ͑x͒ ෇ 1 ϩ 4x Ϫ x 2 b x c 46. f ͑x͒ ෇ 1͞x 2 3 ͑4͒ ; 47. If f ͑x͒ ෇ 2x Ϫ x , ﬁnd f Ј͑x͒, f Љ͑x͒, f ٞ͑x͒, and f ͑x͒. Graph f , f Ј, f Љ, and f ٞ on a common screen. Are the graphs consistent with the geometric interpretations of these derivatives? 48. (a) The graph of a position function of a car is shown, where 42. The ﬁgure shows graphs of f, f Ј, f Љ, and f ٞ. Identify each curve, and explain your choices. y s is measured in feet and t in seconds. Use it to graph the velocity and acceleration of the car. What is the acceleration at t ෇ 10 seconds? s a b c d x 100 0 10 20 t (b) Use the acceleration curve from part (a) to estimate the jerk at t ෇ 10 seconds. What are the units for jerk?

Chapter 2 Limits and Derivatives

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