Strictly increasing or strictly decreasing function

Question

find the intervals in which the function is strictly increasing or decreasing f(x)= (x+1)³(x-1)³

Answer 1

f(x) = (x+1)³ (x-1)³

f'(x) = 3(x+1)² (x-1)³ + 3(x+3)³(x-1)²

= 3(x+1)²(x-1)²(x-1+x+1)

= 6x(x+1)²(x-1)²

∵ f'(x) > 0 when x > 0 & x ≠ 1

& f'(x) < 0 when x < 0 & x ≠ -1

Hence,

f(x) is strictly increasing in (0,∞) - {1}

& stictly decreasing in (-∞,0) - {-1}