# samplemt1 - SOLUTIONS TO MIDTERM 1: MATH 100, SECTION 107...

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SOLUTIONS TO MIDTERM 1: MATH 100, SECTION 107 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 . –1 0 1 2 3 –1 1 2 3 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 )= q x +1 . (c) f ( x )= ( x - 1 + x )( 3 x 2 - 2 x +10 ) . Date : October 2, 2002. 1

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2 SOLUTIONS TO MIDTERM 1: MATH 100, SECTION 107 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 )= 1 2 ( x +1 ) - 1 2 ± 1 2 x ² . (c) f 0 ( x )=( - x - 2 + 1)(3 x 2 - 2 x + 10) + ( x - 1 + x )(6 x - 2) . QUESTION 3: [4 marks] (a) State the tangent line approximation for a function f ( x )atthepo int x 0 .
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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 University .

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samplemt1 - SOLUTIONS TO MIDTERM 1: MATH 100, SECTION 107...

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