Find the intervals in which the function f given by f(x)=2x^3-3x^2-36x+7 is (a) strictly increasing, (b) strictly decreasing.
Find the intervals in which the function f given by f(x)=2x^3-3x^2-36x+7 is (a) strictly increasing, (b) strictly decreasing.

(a) Given: 

   = 

    ……….(i)

Now 

  or 

  or 

Therefore, we have sub-intervals are  and 

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

 > 0

Therefore,  is strictly increasing in 

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

 < 0

Therefore,  is strictly decreasing in 

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

 > 0

Therefore,  is strictly increasing in 

Hence, (a)  is strictly increasing in  and 

(b)  is strictly decreasing in