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#