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Home  >>  CBSE XII  >>  Math  >>  Application of Derivatives
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Let the $f:R\rightarrow R$ be defined by $f(x)=2x+\cos x,$then

$\begin{array}{1 1} (A)\;\text{has a minimum at $x=\pi$} \\ (B)\;\text{has a maximum,at x=0}\\(C)\;\text{is a decreasing function} \\ (D)\;\text{is an increasing function}\end{array} $

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Step 1
$f(x)=2x+ \cos x$
differentiating w.r.t $x$
$f'(x)=2- \sin x$
But we know the range of $ \sin \theta$ is $-1 < x < 1$
hence this implies that
$ f'(x) > 0$ for all values of $x$
Hence it is an increasing function.
The correct answer is D
answered Aug 11, 2013 by thanvigandhi_1
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