Rev1_pdf - rabbani(tar547 Review 1 Fouli(58395 This...

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rabbani (tar547) – Review 1 – Fouli – (58395) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points If f is a function defined on ( 2 , 2) whose graph is 1 2 1 2 1 2 1 2 which of the following is the graph of its derivative f ? 1. 1 2 1 2 1 2 1 2 2. 1 2 1 2 1 2 1 2 3. 1 2 1 2 1 2 1 2 4. 1 2 1 2 1 2 1 2 5. 1 2 1 2 1 2 1 2 correct 6. 1 2 1 2 1 2 1 2 Explanation: Since the graph on ( 2 , 2) consists of straight lines joined at x = 1 and x = 1, the derivative of f will exist at all points in ( 2 , 2) except x = 1 and x = 1, eliminating the answer whose graph contain filled dots at x = 1 and x = 1. On the other hand, the graph of f (i) has slope 2 on ( 2 , 1), (ii) has slope 1 on ( 1 , 1), and (iii) has slope 2 on (1 , 2).
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rabbani (tar547) – Review 1 – Fouli – (58395) 2 Consequently, the graph of f consists of the horizontal lines and ‘holes’ in 1 2 1 2 1 2 1 2 002 10.0 points For which values of x is the function f ( x ) = x 2 x 2 + 3 not continuous? 1. x = 2 , 3 2. f is continuous for all x correct 3. x = 3 , 3 4. x = 3 5. x = 3 6. x = 2 Explanation: Because f is a rational function it will fail to be continuous only at zeros of the denomi- nator. But there are no real solutions to x 2 = 3 , so the function f is continuous for all values of x . 003 10.0 points Below is the graph of a function f . -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 2 4 6 2 4 6 2 4 6 8 2 4 Use the graph to find all values of x at which f is continuous but not differentiable. 1. No such values 2. x = 2 , 0 3. x = 0 correct 4. x = 0 , 3 5. x = 2 , 0 , 3 Explanation: A function is continuous but not differen- tiable at a point if and only if the function has a cusp (wedge) at that point. In the graph above the only such point is x = 0 . Notice that f fails to be continuous at x = 2 and x = 3. keywords: not differentiable, discontinuity, continuous, graph 004 10.0 points Determine f ( x ) when f ( x ) = 4 x 9 + 3 x 4 9 π. 1. f ( x ) = 4 x 9 + 12 x 3 9
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rabbani (tar547) – Review 1 – Fouli – (58395) 3 2. f ( x ) = 36 x 8 + 12 x 3 9 π 3. f ( x ) = 36 x 8 + 12 x 3 correct 4. f ( x ) = 36 x 8 + 12 x 3 9 πx 5. f ( x ) = 36 x 8 + 3 x 4 Explanation: By linearity of differentiation and the rule ( x
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