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# Test 2B - ≤-1 x 1 2 if x>-1 3 Exercise 2 15 points Find...

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Test 2, Version B Math 1501, Fall 02. Prof. W. Gangbo * September 29, 2002 Student Name: Student Section: Teaching Assistant Name: Instructions. You are to work independently these exercises for the next fourty ﬁve minutes (45 mn.). You may not use any textbook or your class notes during the text. Read carefully each exercise and show all your work. * School of Mathematics, Georgia Institute of technology. 1

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Exercise 1 ( 25 points ) (a) ( 10 points ) Assume that f ( x )= 5 - x. Find f 0 (1) by forming the diﬀerence quotient f (1 + h ) - f (1) h and taking the limit as h 0 . 2
(b) ( 15 points )Saywhe the ro rno t f 0 ( - 1) exists. Justify your answer by comparing f 0 - ( - 1) to f 0 + ( - 1) . Here, f ( x )= ±

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Unformatted text preview: ≤ -1 ( x + 1) 2 if x >-1 . 3 Exercise 2 ( 15 points ) Find the points where the tangent line to the graph of x → f ( x ) = x 3-3 x is perpendicular to the line 5 y-3 x-8 = 0 . 4 Exercise 3 ( 20 points ) An object moves along a coordinate line, its position at each time t ≥ 0 is given by x ( t ) = t + 5 t + 2 . Determine when, if ever, the object changes direction. 5 Exercise 4 ( 15 points ) Find f ”(1) where f ( x ) = ( x 2-5 x + 2) 10 . 6 Exercise 5 ( 25 points ) Find dy dx and d 2 y dx 2 at ( x, y ) = (-5 π 6 ,-5 π 6 ) knowing that cos( x + 2 y ) = 0 . 7...
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Test 2B - ≤-1 x 1 2 if x>-1 3 Exercise 2 15 points Find...

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