JEE Mathematics/ Lakshmikanta Satapathy/ Application of Derivative/ Increasing and decreasing functions part 2/ JEE question on intervals for increasing and decreasing functions solved

1. Physics Helpline
L K Satapathy
Increasing / Decreasing Functions 2

2. Physics Helpline
L K Satapathy
Application of Derivative 4
Increasing and Decreasing Functions
Questions
1. The function defined by is strictly increasing in the
intervals
3 2
( ) 2 3 36 7f x x x x   
2. The function defined by is strictly decreasing in the intervals2
( ) [ ( 2)]f x x x 
(a) (- , -2) and (-2 , 3) (b) (-2 , 3) and (3 , )
(c) (- , -2) and (3 , ) (d) (- , -1) and (2 , )
(a) (- , 0) and (1 , 2) (b) (- , 0) and (2 , )
(c) (- , 1) and (2 , ) (d) (0 , 1) and (2 , )

3. Physics Helpline
L K Satapathy
Application of Derivative 4
Increasing and Decreasing Functions
Answer-1 3 2
( ) 2 3 36 7f x x x x   
2 2
( ) 6 6 36 6( 6) 6( 3)( 2)f x x x x x x x         
2 3
( , 2)  ( 2, 3) (3, )
( ) 0 6( 3)( 2) 0 3 , 2f x x x x x         
( ) 6( 2)( 3)f x x x   
( , 2)x    f (x) = (x + 2) (x – 3) = (–).(–) = +ve (increasing)
( 2 , 3)x   f (x) = (x + 2) (x – 3) = (+).(–) = –ve (decreasing)
(3 , )x   f (x) = (x + 2) (x – 3) = (+).(+) = +ve (increasing)
f is strictly increasing in (- ,-2) , (3 , )
Correct option = (c)

4. Physics Helpline
L K Satapathy
Application of Derivative 4
Increasing and Decreasing Functions
Answer-2
( ) 4 ( 1)( 2)f x x x x   
( ,0)x   f (x) = 2x (x –1) (x – 2) = (–).(–).(–) = –ve (decreasing)
(0,1)x
(1,2)x
f is strictly decreasing in (- ,0) , (1 , 2)
2
( ) [ ( 2)]f x x x 
( ) 2 ( 2)[( 2) ] 2 ( 2)(2 2) 4 ( 1)( 2)f x x x x x x x x x x x          
( ) 0 4 ( 1)( 2) 0 0 , 1, 2f x x x x x x x         
1 2
( ,0) (0,1) (2, )(1,2)
0
(2, )x 
 f (x) = 2x (x –1) (x – 2) = (+).(–).(–) = +ve (increasing)
 f (x) = 2x (x –1) (x – 2) = (+).(+).(–) = –ve (decreasing)
 f (x) = 2x (x –1) (x – 2) = (+).(+).(+) = +ve (increasing)
Correct option = (a)

5. Physics Helpline
L K Satapathy
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