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