Calculus Chapter 3 Smartboard Review with Navigator.notebook. November 04, What is the slope of the line segment?

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1 1 What are the endpoints of the red curve segment? alculus: The Mean Value Theorem ( 3, 3), (0, 0) ( 1.5, 0), (1.5, 0) ( 3, 3), (3, 3) ( 1, 0.5), (1, 0.5) Grade: 9 12 Subject: ate: Mathematics «date» 2 What is the slope of the line segment? 3 What is the average slope of the red curve segment? 3 1/3 1/ t which of the following points is the derivative equal to the average slope of the red curve segment? 5 Given a segment of a curve, what is the basic idea of the Mean Value Theorem? ( 2.75, 0) (0, 3) (1, 2) (4.75, 0) t the midpoint of the segment, the derivative equals the average slope of the segment. t some point on the segment, the derivative equals the intermediate value of the function of the segment. t some point on the segment, the intermediate value of the function equals the derivative. t some point on the segment, the derivative equals the average slope of the segment. 1

2 6 What is the average slope of the segment that begins at ( 1, 2) and ends at (1, 2)? 7 Which statement below, if true about the red segment below, would confirm the Mean Value Theorem? The derivative is equal to 0.5 at least once The derivative is equal to 0.5 at least once. The derivative is equal to 0 at least once. The derivative is equal to 2 at least once. 8 The derivative of the function below is x 2 2x. Which equation below, when solved, will find x values where the derivative is equal to the average slope of the red segment? 9 ccording to the Mean Value Theorem, which value must the derivative of the function shown below take on at least once when x is between 2 and 4? x 2 2x = 2 x 2 2x = 0 2x 2 = 2 2x 2 = 0 1/3 0 1/ On which interval is the average slope of the function shown below not equal to 2? alculus: Local Minima and Maxima [ 2, 0] [ 2, 2] [0, 2] Grade: 9 12 Subject: Mathematics ate: 11/4/2011 [0, 4] 2

3 1 What is the local maximum? 2 What is the local minimum? Point Point Point Point Point Point Point Point 3 The graph of f(x) is shown. The derivative of f(x) is = 0.75(x 3)(x 1). For which value below does f(x) have a local maximum? 4 The graph of f(x) is shown. The derivative of f(x) is = 0.75(x 3)(x 1). For which value below does f(x) have a local minimum? x = 1 x = 3 x = 6 x = x = 1 x = 3 x = 6 x = 5 What is the local maximum? 6 What is the local minimum? f(x) = 0.25x(x 3) y = 4.0 y = 2.0 y = 1.0 y = 4.0 y = 2.0 y = 1.0 f(x) = 0.25x(x 3) y = 2.0 = 0.75(x 3)(x 1) y = 2.0 = 0.75(x 3)(x 1) 3

4 7 The graph of the derivative of f(x) is shown below. For which value below does f(x) have a local maximum? 8 What is the x value where the local minimum occurs? x = 2 x = 0.5 x = 0 x = What is the x value where the local maximum occurs? 10 What is the x value where the local minimum occurs? Which statement is false? alculus: Inflection Points and oncavity x 3 has an inflection point at x = 0 x 2 has one inflection point at x = 0 x 4 has no inflection points cos x has an infinite number of inflection points Grade: 9 12 Subject: Mathematics ate: 11/4/2011 4

5 1 Which statement is true? 2 For which interval is f // (x) positive? The first derivative is 0 at an inflection point. n inflection point is where the second derivative changes sign. n inflection point is where the first derivative changes sign. The second derivative is positive at an inflection point. [ 3, 3] [ 3, 0] [1, 3] [0, 3] f(x) = 0.01 x 5 3 For which interval is f // (x) negative? 4 t what value of x does the sign of f (x) change? f(x) = 0.01 x 5 f(x) = 0.01 x 5 [ 3, 1] [ 3, 0] [0, 3] [1, 3] For what interval is f(x) concave up? 6 For which values of x does the concavity of f(x) change? g(x) = x 3 3x [2, 3] [1, 3] [0, 2] [ 1, 1] 1, 0, 1 2, 0, 2 4, 2, 0, 2, 4 3, 1, 1, 3 5

6 7 t which value of x does the concavity of h(x) change? 8 t which value of x does g(x) change from concave down to concave up? h (x) = 2x 2 g (x) = (x 1) t which value of x does g(x) change from concave up to concave down? g (x) = (x 1)

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