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

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Answer 1 · 2017-01-26T05:43:02

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

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

$F'(x)=3*(x^2-1)^2*2x$

$=6x(x^2-1)^2$

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

$6x(x^2-1)^2>0$

that's

$x>0$

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