Example ( a ) You are given the following information about a function f ( x ) f ( x ) 3 x 5 1 5 x 4 5 x 3 4 5 x 2 2 0 f ' ( x ) 1 5 x ( x 2 ) ( x 3 ) ( x 1 ) f ' ' ( x ) 3 0 ( 1 x ) ( 2 x 2 4 x 3 ) 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 function g ( x ) g ( x ) 3 x 4 4 x 3 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 function h ( x ) that passes through the points ( 1 , 3 ) and ( 3 , 0 ) and meets the following requirements Note that there are many possible graphs that would meet these conditions you are only being asked to sketch one such graph Be sure to label maxima, minima, point ( s ) of inflection, and any other features of interest on your graph h ( 1 ) is a global maximum value h ' ( x ) 0 over ( , 1 ) ( 3 , ) , h ' ( x ) 0 over ( 1 , 3 ) , h ' ( 1 ) 0 h ' ( 3 ) h ' ' ( x ) 0 over ( 2 , 4 ) , h ' ' ( x ) 0 over ( , 2 ) ( 4 , ) , h ' ' ( 2 ) 0 h ' ' ( 4 )

Question

Example ( a ) You are given the following information about a function f ( x )   f ( x )     3 x 5 1 5 x 4   5 x 3   4 5 x 2   2 0 f  ' ( x )     1 5 x ( x   2 ) ( x   3 ) ( x 1 ) f  '  ' ( x )   3 0 ( 1   x ) ( 2 x 2   4 x   3 ) 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 function g ( x )   g ( x )   3 x 4   4 x 3 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 function h ( x ) that passes through the points ( 1 , 3 ) and ( 3 , 0 ) and meets the following requirements  Note that there are many possible graphs that would meet these conditions  you are only being asked to sketch one such graph  Be sure to label maxima, minima, point ( s ) of inflection, and any other features of interest on your graph  h ( 1 ) is a global maximum value h  ' ( x )   0 over (   , 1 ) ( 3 , )   , h  ' ( x )   0 over ( 1 , 3 )   , h  ' ( 1 )   0   h  ' ( 3 ) h  '  ' ( x )   0 over ( 2 , 4 )   , h  '  ' ( x )   0 over (   , 2 ) ( 4 , )   , h  '  ' ( 2 )   0   h  '  ' ( 4 )

HelloExperts · Accepted Answer

The Answer is in the image, click to view...

Example ( a ) You are given the following information about a function f ( x ) : f ( x ) = - 3

Step by Step Solution

1 Understanding Responsive Design Principles

Related Multivariable Calculus Questions