Consider the following statements S and R. S: Both $$sin$$⁡x and $$cos$$⁡x are decreasing functions in π$$2$$,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?

Question

Consider the following statements S and R. S: Both $$sin$$⁡x and $$cos$$⁡x are decreasing functions in π$$2$$,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?

Infinity Learn · Accepted Answer

$$y=cosx$$       or      $$sinxdydx=$$−sinx   or   cosx Both are $$-ve$$ in π$$2$$,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

$Consider the following statements S and R .$
$S : Both \sin x and \cos x are decreasing functions in (\frac{π}{2}, π)$
$R \underline{\underline{If}} a differentiable function decreases in an interval (a, b), then its derivative$ $also decreases in (a, b) .$
Which of the following is true?

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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?

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$Consider the following statements S and R .$
$S : Both \sin x and \cos x are decreasing functions in (\frac{π}{2}, π)$
$R \underline{\underline{If}} a differentiable function decreases in an interval (a, b), then its derivative$ $also decreases in (a, b) .$
Which of the following is true?