FINAL REVIEW 3

# FINAL REVIEW 3 - ngac(xtn62 NewFinalReview01 Gilbert(58365...

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ngac (xtn62) – NewFinalReview01 – Gilbert – (58365) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page – fnd all choices be±ore answering. 001 10.0 points f is a ±unction defned on ( 2 , 2) whose graph is 1 2 1 2 1 2 1 2 which o± the ±ollowing is the graph o± 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 correct 5. 1 2 1 2 1 2 1 2 6. 1 2 1 2 1 2 1 2 Explanation: Since the graph on ( 2 , 2) consists o± straight lines joined at x = 1 and x = 1, the derivative o± f will exist at all points in ( 2 , 2) except x = 1 and x = 1, eliminating the answer whose graph contain flled dots at x = 1 and x = 1. On the other hand, the graph o± 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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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 3 x 2 + 3 not continuous? 1. x = 3 2. f is continuous for all x correct 3. x = 3 4. x = 3 , 3 5. x = 3 , 3 6. x = 3 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 . 2 4 6 2 4 6 2 4 6 8 2 4 Use the graph to ±nd all values of x at which f is continuous but not di²erentiable. 1. x = 0 , 3 2. x = 3 , 0 , 3 3. No such values 4. x = 3 , 0 5. x = 0 correct Explanation: A function is continuous but not di²eren- 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 = 3 and x = 3. keywords: not di²erentiable, discontinuity, continuous, graph 004 10.0 points Determine f ( x ) when f ( x ) = 9 x 6 4 x 3 3 π. 1.
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FINAL REVIEW 3 - ngac(xtn62 NewFinalReview01 Gilbert(58365...

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