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Section 2.6 Day 2 Inflection Points and the Second Derivative I can describe the graph of f (x) given f (x). I can analyze the graph of f (x) in order.

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Presentation on theme: "Section 2.6 Day 2 Inflection Points and the Second Derivative I can describe the graph of f (x) given f (x). I can analyze the graph of f (x) in order."— Presentation transcript:

1 Section 2.6 Day 2 Inflection Points and the Second Derivative I can describe the graph of f (x) given f (x). I can analyze the graph of f (x) in order to draw conclusions about the graph of f (x). You are given the graph of f (x). For each of the graphs below, answer the following questions: 1.What can you say about f(x)? 2.What can you say about f(x)? a. b. Day 4 (Answer these on your bell ringer sheet)

2 A. For what value(s) of x is undefined? B.On what interval(s) is f(x) concave down?. C.On what intervals is increasing? D. On what intervals is This is the graph of f(x) on (-3, 3) (-1, 1) (-3, -1), (1, 3) (-3, -1), (0, 1) -1, 1

3 A. For what value(s) of x is undefined? B.On what interval(s) is f(x) concave down?. C.On what intervals is increasing? D. On what intervals is This is the graph of on (-3, 3) (-3, -1), (0, 1) (-1, 0), (1, 3) none

4 A.On what interval(s) is f(x) concave up? B.List the value(s) of x for which f(x) has a point of inflection. C.For what value(s) of x is ? This is the graph of on (-3, 3) none -1, 1 (-3, -1), (-1, 1), (1, 3)

5 A. For what value(s) of x is f (x) = 0? B.On what intervals is f (x) > 0? C. On what intervals is f (x) < 0? D.Find the x-coordinate of the point(s) of inflection. This is the graph of f(x) on (-2, 2) -0.5, 0.5 (-2, -0.5), (0.5, 2) (-2, 0) x = 0

6 A. For what value(s) of x is f (x) = 0? B.On what intervals is f(x) decreasing? C. On what intervals is f (x) < 0? D.Find the x-coordinate of the point(s) of inflection. This is the graph of f (x) on (-2, 2). -1, 0, 1 (-2, -1), (0, 1) (-0.5, 0.5) -0.5, 0.5

7 A. On what interval(s) is f(x) concave up? B.Find the x-coordinate of the point(s) of inflection. C.On what interval(s) is f (x) > 0? This is the graph of f (x) on [-1, 5]. [-1, 1), (3, 5] 1, 3 [-1, 1), (3, 5]

8 For what value(s) of x does f (x) not exist? On what interval(s) is f(x) concave down? On what interval(s) is f (x) > 0? Where is/are the relative minima on [-10, 3]? This is the graph of f (x) on [-10, 3]. none (-10, 0), (0, 3)

9 Which of the following is/are true about the function f if its derivative is defined by I) f is decreasing for all x < 4 II) f has a local maximum at x = 1 III) f is concave up for all 1 < x < 3 A) I only B) II only C) III only D) II and III only E) I, II, and III increasing NO TRUE

10 The graph of the second derivative of a function f is shown below. Which of the following are true about the original function f? I) The graph of f has an inflection point at x = -2 II) The graph of f has an inflection point at x = 3 III) The graph of f is concave down on the interval (0, 4) A) I only B) II only C) III only D) I and II only E) I, II and III NO YES NO

11 Which of the following statements are true about the function f, if its derivative f is defined by I) The graph of f is increasing at x = 2a II) The function f has a local maximum at x = 0 III) The graph of f has an inflection point at x = a A)I only B) I and II only C) I and III only D) II and III only E) I, II and III NO Use a = 2


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