Test whether the function f(x)=x-cos x where x€(0, pi) is increasing

1.	Test whether the function f(x)=x-cos x where x€(0, pi) is increasing or decreasing
Answer» $\displaystyle\huge\red{\underline{\underline{Solution}}}$ TO CHECK $\sf{ The \: function \: f(<klux>X</klux>) = x - \cos x \: \: \: where \: \: x \in(0, \pi) }$ is increasing or decreasing CONCEPT TO BE IMPLEMENTED A function f (x) is increasing in an interval [ a, b ] f'(x) > 0 for every point on that interval [ a, b] A function f (x) is decreasing in an interval [ a, b ] f'(x) < 0 for every point on that interval [ a, b] CALCULATION Here the given function is $\sf{ f(x) = x - \cos x \: \: \: where \: \: x \in(0, \pi) }$ Differentiating both sides with respect to x we get $\sf{ f \: '(x) = 1 + \sin x \: }$ $\sf{Since \: for \: every \: \: x \in (0,\pi) \: we \: get \: f'(x) > 0 }$ $\sf{ Hence \: the \: function \: f(x) = x - \cos x \: \: \: where \: \: x \in(0, \pi) }$ is increasing ━━━━━━━━━━━━━━━━ *LEARN MORE FROM BRAINLY* The coordinates (x,y) of a PARTICLE moving along a plane curve at any time t are given by y'+ 2x = sin 2t , x' -2 y = cos 2t brainly.in/question/14323222

Test whether the function f(x)=x-cos x where x€(0, pi) is increasing or decreasing

Answer»

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

$\sf{ The \: function \: f(<klux>X</klux>) = x - \cos x \: \: \: where \: \: x \in(0, \pi) }$

is increasing or decreasing

A function f (x) is increasing in an interval [ a, b ] f'(x) > 0 for every point on that interval [ a, b]

A function f (x) is decreasing in an interval [ a, b ] f'(x) < 0 for every point on that interval [ a, b]

Here the given function is

$\sf{ f(x) = x - \cos x \: \: \: where \: \: x \in(0, \pi) }$

Differentiating both sides with respect to x we get

$\sf{ f \: '(x) = 1 + \sin x \: }$

$\sf{Since \: for \: every \: \: x \in (0,\pi) \: we \: get \: f'(x) > 0 }$

$\sf{ Hence \: the \: function \: f(x) = x - \cos x \: \: \: where \: \: x \in(0, \pi) }$

is increasing

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LEARN MORE FROM BRAINLY

The coordinates (x,y) of a PARTICLE moving along a plane curve at any time t are given by