Section B ( 41 marks ) 7 . A rectangular box has length 4x cm , width 2x cm and height y cm , where x , y � 0. It is given that the sum of the length and the height of the rectangular box is 20 cm .
( a ) Write down an expression for y in terms of x .
( b ) Express V in terms of x , where
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V cm is the volume of the rectangular box . [ 2 ]
( c ) Find d V dx . [ 2 ]
( d ) Find the value of x when V attains its maximum , justifying the answer . [ 7 ]
( e ) Hence , find the maximum volume . [ 2 ]
( f ) Write down the height of the rectangular box when V attains its maximum .
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