( a ) You are given the following information about a function f ( x ) f ( x ) 2 x 5 5 x 4 1 0 x 3 f ' ( x ) 1 0 x 2 ( x 3 ) ( x 1 ) Describe all intervals on which f ( x ) is increasing or decreasing Identify any maxima or minima ( x coordinates only ) , and indicate whether they are local or global extrema Be sure to support your answers ( b ) You are given the following information about a function g ( x ) g ( x ) x 4 3 x 3 3 x 2 x g ' ( x ) 4 x 3 9 x 2 6 x 1 g ' ' ( x ) 6 ( 2 x 1 ) ( x 1 ) Describe all intervals on which g ( x ) is concave up or concave down Identify any inflection points ( x coordinates only ) Be sure to support your answers ( c ) Draw a graph of a continuous function h ( x ) that satisfies the following conditions h ( 0 ) 4 , h ( 2 ) 0 lim x h ( x ) 4 h ' ( 0 ) 0 , h ' ( x ) 0 o n ( , 0 ) , h ' ( x ) 0 o n ( 0 , ) h ' ' ( 1 ) h ' ' ( 1 ) 0 , h ' ' ( x ) 0 o n ( , 1 ) ( 1 , ) , h ' ' ( x ) 0 o n ( 1 , 1 )

Question

( a ) You are given the following information about a function f ( x )   f ( x )   2 x 5   5 x 4   1 0 x 3 f  ' ( x )   1 0 x 2 ( x   3 ) ( x 1 ) Describe all intervals on which f ( x ) is increasing or decreasing  Identify any maxima or minima ( x   coordinates only ) , and indicate whether they are local or global extrema  Be sure to support your answers  ( b ) You are given the following information about a function g ( x )   g ( x )   x 4   3 x 3 3 x 2   x g  ' ( x )   4 x 3   9 x 2 6 x   1 g  '  ' ( x )   6 ( 2 x   1 ) ( x   1 ) Describe all intervals on which g ( x ) is concave up or concave down  Identify any inflection points ( x   coordinates only )   Be sure to support your answers  ( c ) Draw a graph of a continuous function h ( x ) that satisfies the following conditions  h ( 0 )     4   , h (   2 )   0 lim x h ( x )   4 h  ' ( 0 )   0   , h  ' ( x ) 0 o n (   , 0 )   , h  ' ( x )   0 o n ( 0 , ) h  '  ' (   1 )   h  '  ' ( 1 )   0   , h  '  ' ( x ) 0 o n (   ,   1 ) ( 1 , )   , h  '  ' ( x )   0 o n (   1 , 1 )

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( a ) You are given the following information about a function f ( x ) : f ( x ) = 2 x 5

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1 Understanding Responsive Design Principles

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