Consider the following statements S and R :
S: Both sin x and cos x are decreasing functions in the interval (π/2, π).
R: If a differentiable function decreases in an interval a, b, then its derivative also decreases in (a, b)
Which of the following is true?
Answer & explanation
Correct answer: option 4
It is evident that both sin x and cos x are decreasing functions in the interval $(\pi / 2, \pi)$. So, S is correct.
Statement R is not correct, because sin x is decreasing in the interval $(\pi / 2,3 \pi / 2)$ but its derivative i.e. cos x is not so.