Consider the following statements $S$ and $R$ : $S$: Both $\sin x$ and $\cos x$ are decreasing function in $\left( \frac{\pi}{2},\pi \right)$ $R$: If a differentiating function decreases in $(a,\ b)$ then its derivative also decreases in $(a,\ b)$ Which of the following is true?

Question

Dr. Abubacker · Accepted Answer

(d)
We know that, $\sin x$ and $\cos x$ decrease in $\frac{\pi}{2} < x < \pi$, so the statement $S$ is correct
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The statement $R$ is incorrent which is clear from the graph that $f(x)$ is differentiable in $(a,\ b)$
Also, $a < x_{1} < x_{2} < b$
But $f^{''}\left( x_{1} ight) = 	an\phi_{1} < 	an\phi_{2} = f^{''}(x_{2})$
$\Rightarrow$ Derivate is increasing

Q. Consider the following statements $S$ and $R$ : $S$: Both $\sin x$ and $\cos x$ are decreasing function in $\left( \frac{\pi}{2},\pi \right)$ $R$: If a differentiating function decreases in $(a,\ b)$ then its derivative also decreases in $(a,\ b)$ Which of the following is true?

Explanation

Reviewed by Dr. Abubacker

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