How do you find the intervals of increasing/decreasing of F(x)= (x^2-1)^3?

Jan 26, 2017

F(x) is increasing if x>0 and decreasing if x<0

Explanation:

You will find the intervals of increasing/decreasing of F(x), by studying the positivity of its first derivative:

$F ' \left(x\right) = 3 \cdot {\left({x}^{2} - 1\right)}^{2} \cdot 2 x$

$= 6 x {\left({x}^{2} - 1\right)}^{2}$

The intervals where it is positive are those where F(x) is increasing, then you would solve:

$6 x {\left({x}^{2} - 1\right)}^{2} > 0$

that's

$x > 0$