Find the intervals in which the function f given by is

(i) Increasing (ii) decreasing.

It is given that f(x) =

Then, f’(x) =0

⇒ 3x⁶ - 3 = 0

⇒ x⁶ = 1

⇒ x = 1

Now, the points x =1 and x = - 1 divide the real line into three disjoint intervals

( - ∞, - 1), ( - 1,1) and (1,∞).

In interval ( - ∞, - 1) and (1,∞) when x < - 1 and x > 1 then f’(x) >0

Therefore, when x < - 1 and x > 1, f is increasing.

And, in interval ( - 1,1) when - 1< x < 1 then f’(x) < 0.

Therefore, when - 1 < x < 1, f is decreasing.