Given #f'(x) = (x+1)(x-2)²g(x)# where #g# is a continuous function and #g(x) < 0# for all #x#. On what interval(s) is #f# decreasing?

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Answer 1 · 2016-09-28T22:52:05

#x > -1#

For #f(x)# to be decreasing is necessary that

#f'(x) < 0# so

#(x+1)(x-2)^2g(x) < 0#

If #g(x) < 0 forall x in RR# then this is equivalent to

#(x+1)(x-2)^2 > 0#

Here #(x-2)^2 ge 0# so the condition is

#x+1 > 0# or #x > -1#