The minimum value of the function $f(x) = {x^{10}} + {x^2} + \frac{1}{{{x^{12}}}} + \frac{1}{{\left( {1\ +\ {{\sec }^{ - 1}}\ x} \right)}}$ is
The minimum value of the function $f(x) = {x^{10}} + {x^2} + \frac{1}{{{x^{12}}}} + \frac{1}{{\left( {1\ +\ {{\sec }^{ - 1}}\ x} \right)}}$ is
- A
$\frac{{\pi\ +\ 4}}{{\pi\ +\ 1}}$
- B
$\frac{{3\pi\ +\ 4}}{{\pi\ +\ 1}}$
- C
$\frac{{\pi\ +\ 4}}{{3\pi\ +\ 1}}$
- D
$3$
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