3 . The temperature Q of a substance at time t is given by t � 0 .
3 2 Q( t) t 12t 36t � � � , where
( a ) Find the t -intercepts of Q .
( b ) ( i ) Find Q� () t .
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( ii ) Solve the equation Q�( t) � 0 .
( iii ) Hence , find the value of � when Q is at a local maximum , justifying that it is a maximum .
( iv ) Write down the maximum value of Q .
Let R( t) �Q( t) � 20 .
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( c ) ( i ) Find the minimum value of R .
( ii ) Write down the corresponding value ( s ) of t . [ 3 ]
4 . The price P of a share at time t is given by 0 �t � 12 .
3 2
P( t) � �t �9t � 24t � 720 , where
( a ) Find the t -intercept of P .
( b ) ( i ) Find P� () t .
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( ii ) Solve the equation P�( t) � 0.
( iii ) Hence , find the value of � when P is at a local minimum , justifying that it is a minimum .
( iv ) Write down the minimum value of P .
It is given that P( 0 ) � 720 .
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( c ) ( i ) Write down P ( 4 ) .
( ii ) Hence , write down the maximum value of P .
Let Q( t) �P( t � 3 ) . ( d ) Find the corresponding value of t when Q attains its maximum .
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