Question

The local minimum value of the function \[ f(x)=2x-3\tan^{-1}x \] is

• A. \(3\tan^{-1}\!\left(\dfrac1{\sqrt2}\right)-\sqrt2\)
• B. \(\sqrt2-3\tan^{-1}\!\left(\dfrac1{\sqrt2}\right)\)
• C. \(3\tan^{-1}(\sqrt2)-\dfrac1{\sqrt2}\)
• D. \(\dfrac1{\sqrt2}-3\tan^{-1}(\sqrt2)\)

Hint:

For local extrema, \[ \boxed{f'(x)=0} \] gives the critical points, while \[ \boxed{ f''(x)>0 } \] indicates a local minimum and \[ \boxed{ f''(x)<0 } \] indicates a local maximum.

Answer 1

The Correct Option is B