Find the intervals in which the following functions are strictly increasing or decreasing:
Find the intervals in which the following functions are strictly increasing or decreasing:

(a)    

(b)    

SOLUTION:

(a) Given: 

     ……….(i)

Now 

 

Therefore, we have two sub-intervals  and 

For interval  taking  (say), from eq. (i),  < 0

Therefore,  is strictly decreasing.

For interval  taking  (say), from eq. (i),  > 0

Therefore,  is strictly increasing.

(b) Given: 

  =   ……….(i)

Now 

 

Therefore, we have two sub-intervals  and 

For interval  taking  (say), from eq. (i),

 > 0

Therefore,  is strictly increasing.

For interval  taking  (say), from eq. (i),

 < 0

Therefore,  is strictly decreasing.