Let us assume the functions f ( x ) and g ( x ) given by f ( x ) = tan x − x and g ( x ) = x − sin x , for 0 0 and g ′ ( x ) > 0 , ∀ x ∈ ( 0 , 2 π ) ⇒ f ( x ) > f ( 0 ) and g ( x ) > g ( 0 ) ∀ x ∈ ( 0 , 2 π ) ⇒ tan x − x > 0 and x − sin x > 0 , ∀ x ∈ ( 0 , 2 π ) ⇒ tan x > x and x > sin x , ∀ x ∈ ( 0 , 2 π ) ⇒ sin x < x < tan x , ∀ x ∈ ( 0 , 2 π )

Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-MinimaMedium2 minPYQ_2015

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Let us assume the functions $f (x)$ and $g (x)$ given by $f (x) = tan x - x$ and $g (x) = x - sin x,$ for $0 < x < \frac{π}{2}$ Now, $f^{'} (x) = sec^{2} x - 1$ and $g^{'} (x) = 1 - cos x$ $\Rightarrow f (x) > 0$ and $g^{'} (x) > 0, \forall x \in (0, \frac{π}{2})$ $\Rightarrow f (x) > f (0)$ and $g (x) > g (0) \forall x \in (0, \frac{π}{2})$ $\Rightarrow tan x - x > 0$ and $x - sin x > 0,$ $\forall x \in (0, \frac{π}{2})$ $\Rightarrow tan x > x$ and $x > sin x, \forall x \in (0, \frac{π}{2})$ $\Rightarrow sin x < x < tan x, \forall x \in (0, \frac{π}{2})$

Stream:BITSATSubject:MathematicsTopic:Application of DerivativeSubtopic:Maxima-Minima

⏱ 2mℹ️ Source: PYQ_2015

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