Try this beautiful problem on Sign change, useful for ISI B.Stat Entrance.
In the interval \((-2\pi, 0)\) the function \(f(x) = sin(1/x^3)\)
But try the problem first...
TOMATO, Problem 709
Challenges and Thrills in Pre College Mathematics
As x becomes \(\leq 1\) and tends to zero then it crosses \(\pi, 2\pi, 3\pi, ….\).can you draw the graph?
Can you now finish the problem ..........
If we draw the graph then we can see that the function \(f(x) = sin(1/x^3)\) crosses many times. Therefore number of sign changes is infinite.
Therefore option \((d)\) is correct.....