Problem Set 04s

Problem Set 04s - Hung Nguyen Problem Set 04 Solution GE...

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Hung Nguyen Problem Set 04 Solution GE 207C 2.7 Derivative as a rate of change 2.8 Derivative as a function 1 1. The graph of f is given below, sketch the graph of the derivative (f’) and f’’ of f? a. Solution: b. Solution: 2. Recently, Stewart drove the 120 kms from Austin to San Antonio, leaving at 12noon and arriving in SA at 1:30pm. He stayed briefly and then started back. The GPS system in his car recorded his distance from Austin in terms of the time of day. It plotted these accurately to scale: Which of the following statements are true? A. At 1:00pm he was braking. B. His average speed between 1:10 and 1:20pm was more than 120 km/hr. 3. Use the definition of a derivative f '( x ) = lim h 0 f ( x + h ) f ( x ) h to differentiate the following functions: a. x x x f + = 1 2 ) ( Solution:
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Hung Nguyen Problem Set 04 Solution GE 207C 2.7 Derivative as a rate of change 2.8 Derivative as a function 2 f '( x ) = lim h 0 f ( x + h ) f ( x ) h = 2 ( x + h ) 1 + x + h ( ) 2 x 1 + x h = 2 x h ( ) 1 + x ( ) 2 x ( ) 1 + x + h ( ) 1 + x ( ) 1 + x + h ( ) h = lim h 0 3 h h 1 + x ( ) 1 + x + h ( ) = 3 1 + x ( ) 2 = f '( x ) b.
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Problem Set 04s - Hung Nguyen Problem Set 04 Solution GE...

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