JEE Advance - Mathematics (2000 - No. 30)
Consider the following statements in $$S$$ and $$R$$
$$S:$$ $$\,\,\,$$$ Both $$\sin \,\,x$$ and $$\cos \,\,x$$ are decreasing functions in the interval $$\left( {{\pi \over 2},\pi } \right)$$
$$R:$$$$\,\,\,$$ If a differentiable function decreases in an interval $$(a, b)$$, then its derivative also decreases in $$(a, b)$$.
Which of the following is true ?
$$S:$$ $$\,\,\,$$$ Both $$\sin \,\,x$$ and $$\cos \,\,x$$ are decreasing functions in the interval $$\left( {{\pi \over 2},\pi } \right)$$
$$R:$$$$\,\,\,$$ If a differentiable function decreases in an interval $$(a, b)$$, then its derivative also decreases in $$(a, b)$$.
Which of the following is true ?
Both $$S$$ and $$R$$ are wrong
Both $$S$$ and $$R$$ are correct, but $$R$$ is not the correct explanation of $$S$$
$$S$$ is correct and $$R$$ is the correct explanation for $$S$$
$$S$$ is correct and $$R$$ is wrong