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chapter4Problems - Chapter 4 The Derivative 4.1 You are...

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Chapter 4 The Derivative 4.1 You are given the following information about the signs of the derivative of a function, f ( x ). Use this information to sketch a (very rough) graph of the function for - 3 < x < 3. x -3 -2 -1 0 1 2 3 f prime ( x ) 0 + 0 - 0 + + 4.2 You are given the following information about the the values of the derivative of a function, g ( x ). Use this information to sketch (very rough) graph the function for - 3 < x < 3. x -3 -2 -1 0 1 2 3 g prime ( x ) -1 0 2 1 0 -1 -2 4.3 What is the slope of the tangent line to the function y = f ( x ) = 5 x + 2 when x = 2? when x = 4 ? How would this slope change if a negative value of x was used? Why? 4.4 Find the equation of the tangent line to the function y = f ( x ) = | x + 1 | at: (a) x = - 1, (b) x = - 2, (c) x = 0. If there is a problem finding a tangent line at one of these points, indicate what the problem is. v.2005.1 - September 4, 2009 1
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Math 102 Problems Chapter 4 4.5 A function f ( x ) has as its derivative f prime ( x ) = 2 x 2 - 3 x (a) In what regions is f increasing or decreasing? (b) Find any local maxima or minima. (c) Is there an absolute maximum or minimum value for this function? 4.6 Sketch the graph of a function f ( x ) whose derivative is shown in Figure 4.1. Is there only one way to draw this sketch? What difference might occur between the sketches drawn by two different students?
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