Which reason justifies the statement below?
1 answer:
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is decreasing on some interval
if
for all
. Similarly,
is increasing on
if
for all
.
On the domain , we have
as the only critical point. So we need to check the sign of on two intervals,
and
.
On , pick any test value. Suppose we take
. Then
, so
is decreasing on this interval.
On , you'd find that
, so
is increasing on this interval.