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# samplemt2 - MIDTERM 1 MATH 100 SECTION 109 WEDNESDAY OCT 7...

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MIDTERM 1: MATH 100, SECTION 109, WEDNESDAY OCT. 7 QUESTION 1: [4 marks] Below you are given the graph of y = f 0 ( x ) for some function y = f ( x ) . Graph the function y = f ( x ) assuming that f (0) = 1 . –3 –2 –1 0 1 x Figure 1. The graph of y = f 0 ( x ) Solution to (1): Figure 2. The graph of y = f ( x ) QUESTION 2: [6 marks] Using the rules of diﬀerentiation ﬁnd the derivatives of the following functions. DO NOT SIMPLIFY YOUR ANSWERS. (a) f ( x )= x 2 +2 x x 3 - x - 1 . (b) f ( x )= 1 x +1 . (c) f ( x )= ( x - 2 + x 2 )( x - x - 1 ) . Date : October 2, 2002. 1

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2 MIDTERM 1: MATH 100, SECTION 109, WEDNESDAY OCT. 7 Solution to (2): (a) f 0 ( x )= ( x 3 - x - 1)(2 x +2) - ( x 2 +2 x )(3 x 2 - 1) ( x 3 - x - 1) 2 . (b) f 0 ( x )= - ( x +1) - 2 ± 1 2 x ² . (c) f 0 ( x )=( - 2 x - 3 +2 x )( x - x - 1 )+( x - 2 + x 2 )(1 + x - 2 ) . QUESTION 3: [4 marks] Let g ( x )=( f ( x )) 3 . You are given that f (0) = 2 and f 0 (0) = - 1 . Find
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## This note was uploaded on 01/12/2010 for the course STAT 100 taught by Professor Denissjerve during the Winter '06 term at San Jose State.

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samplemt2 - MIDTERM 1 MATH 100 SECTION 109 WEDNESDAY OCT 7...

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