If fx- sin x-xcos x - 0- x- and A- fx- B then set of values of -A-B- is

The correct option is C [0, π] Given nbsp; f(x)= sin x xcos x ⇒ f'(x) = cos x cos x+xsin x=xsin x Clearly f'(x) is positive in the given ...

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Byju's Answer

Standard XII

Mathematics

Definition of Functions

If fx= sin ...

Question

If $f (x) = sin x - x cos x, 0 \leq x \leq π$ and $A \leq f (x) \leq B$ then set of values of $[A, B]$ is

[0, \frac{π}{2}]

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[0, 2 π]

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[0, π]

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[- π, π]

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Solution

The correct option is C $[0, π]$
Given $f (x) = sin x - x cos x$
$\Rightarrow f^{'} (x) = cos x - cos x + x sin x = x sin x$
Clearly $f^{'} (x)$ is positive in the given interval
Thus in the interval $0 \leq x \leq π$ $f (x)$ is increasing function.
Thus range of $f (x)$ is $= [f (0), f (π)] = [0, π]$

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If f(x)=sinx−xcosx , 0≤x≤π and A≤f(x)≤B then set of values of [A,B] is

The correct option is C [0,π]Given f(x)=sinx−xcosx⇒f′(x)=cosx−cosx+xsinx=xsinxClearly f′(x) is positive in the given interval Thus in the interval 0≤x≤π f(x) is increasing function.Thus range of f(x) is =[f(0),f(π)]=[0,π]

If $f (x) = sin x - x cos x, 0 \leq x \leq π$ and $A \leq f (x) \leq B$ then set of values of $[A, B]$ is