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Maths-

General

Easy

Question

Consider the following statements $S$ and $R$ :
$S$ : Both $sin invisible function application x$ and $cos invisible function application x$ are decreasing function in $open parentheses fraction numerator pi over denominator 2 end fraction comma pi close parentheses$

$R$ : If a differentiating function decreases in $open parentheses a comma blank b close parentheses$ then its derivative also decreases in $open parentheses a comma blank b close parentheses$

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 for $S$
$S$ is correct and $R$ is the correct explanation for $S$
$S$ is correct, $R$ is wrong

The correct answer is: $S$ is correct, $R$ is wrong

We know that, $sin invisible function application x$ and $cos invisible function application x$ decrease in $fraction numerator pi over denominator 2 end fraction less than x less than pi$ , so the statement $S$ is correct

The statement $R$ is incorrent which is clear from the graph that $f open parentheses x close parentheses$ is differentiable in $open parentheses a comma blank b close parentheses$

Also, $a less than x subscript 1 end subscript less than x subscript 2 end subscript less than b$

But $f to the power of ´ ´ end exponent open parentheses x subscript 1 end subscript close parentheses equals tan invisible function application ϕ subscript 1 end subscript less than tan invisible function application ϕ subscript 2 end subscript equals f to the power of ´ ´ end exponent left parenthesis x subscript 2 end subscript right parenthesis$

$rightwards double arrow$ Derivate is increasing

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