The function f x -lnsin x - x -0- -2- is decreasing in the intervalA- 0- -4B- 0- -2C- 0- -6D- function is non-decreasing

The correct option is D function is non decreasingf(x) = lnsin x ⇒ f'(x) = cos x/sin x nbsp; In the given interval f'(x) ≥ 0 nbsp; Hence the function is no ...

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Standard XII

Mathematics

Continuity in an Interval

The function ...

Question

The function $f (x) = ln sin x \forall x \in (0, \frac{π}{2}]$ is decreasing in the interval

(0, \frac{π}{4})

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(0, \frac{π}{6})

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(0, \frac{π}{2})

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function is non-decreasing

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Solution

The correct option is D function is non-decreasing
$f (x) = ln sin x \Rightarrow f^{'} (x) = \frac{cos x}{sin x}$
In the given interval $f^{'} (x) \geq 0$
Hence the function is non- decreasing.

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Similar questions

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The function f(x)=lnsinx ∀x∈(0,π2] is decreasing in the interval

The correct option is D function is non-decreasingf(x)=lnsinx⇒f′(x)=cosxsinx In the given interval f′(x)≥0 Hence the function is non- decreasing.

The function $f (x) = ln sin x \forall x \in (0, \frac{π}{2}]$ is decreasing in the interval

The correct option is D function is non-decreasing
$f (x) = ln sin x \Rightarrow f^{'} (x) = \frac{cos x}{sin x}$
In the given interval $f^{'} (x) \geq 0$
Hence the function is non- decreasing.