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Question

Functions which are not monotonic throughout their domains could be monotonic in an interval of their domain.


A

True

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B

False

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Solution

The correct option is A

True


Let’s try to answer this question in this way. We know that sin(x) is not a monotonic function. And why do we say that? We say it because it increases in some interval like π2 to π2 and decreases in π2 to 3π2 . So sin(x) is not a monotonic function. But let’s consider these intervals one by one. If we just consider an interval from π2 to π2, can we say that function is monotonically increasing in the interval? We can . This is nothing but saying that sin(x) function is monotonically increasing function in the interval to [π2 to π2 ].

So the function which is not monotonic in the whole domain of it could be monotonic in an interval of its domain.


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