Consider the following statements S and R. S: Both sin⁡x and cos⁡x are decreasing functions in π2,πR If __ a differentiable function decreases in an interval (a,b), then its derivative  also decreases in (a,b). Which of the following is true?

y=cosx       or      sinxdydx=−sinx   or   cosx Both are -ve in π2,π, Hence S is correct. Again, if a differentiable function decreases, then its derivativef'(x)=−ve. It is not necessary that its derivative f′′(x) may be +ve and hence it may be increasing or decreasing.  Hence R is not correct.Hence (4) is the correct answer