Find the minimum value the function f x - 2-16-1 -x -1x

The correct option is B π2 f ( x )=π ^2/16^ 1 ( x ) ( π ^ 1 ( x ) ) #160; #160; #160; #160; #160; #160; =^ 1 ( x )+π ...

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Domain and Range of Basic Inverse Trigonometric Functions

Find the mini...

Question

Find the minimum value the function $f (x) = \frac{π^{2}}{16 {cot}^{- 1} (- x)} - {cot}^{- 1} x$

- \frac{π}{4}

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- \frac{π}{2}

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0

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\frac{π}{2}

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M = \frac{π^{2}}{16 {sin}^{- 1} (- x)} + {cos}^{- 1} x

f (x) = s i n^{- 1} x + 2 t a n^{- 1} x + x^{2} + 4 x + 1

If, $f (x) = c o s [π^{2}] x + c o s [- π^{2}] x,$ where [x] stands for greatest integer function, then

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} - 2 sin x, & - π \leq x \leq \frac{- π}{2} a cos (x) + b, & \frac{- π}{2} < x < 0 - 2 + cos x, & 0 \leq x \leq \frac{π}{2} c sin x, & \frac{π}{2} < x \leq π \end{matrix} ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭

[- π, π],

f (x)

\int_{0}^{x} \frac{d θ}{c o s θ} + \int_{x}^{π / 2} \frac{d θ}{s i n θ}

x \in [0, \frac{π}{2}],

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