Q. Consider the following statments in S and R
S : Both sin x and cos x are decreasing functions in the interval
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 ?

 1859  224 JEE AdvancedJEE Advanced 2000Application of Derivatives Report Error

Solution:

From graph it is clear that both sin x and cos x in the interval are decreasing function.
S is correct.
To disprove R let us consider the counter example :
f (x) = sin x on
so that
Again from graph it is clear that f (x) is increasing on but is decreasing on
R is wrong.

Solution Image