Find the critical numbers for $f ( x ) = \tan ^ { - 1 } \left( \frac { x } { a } \right) - \tan ^ { - 1 } \left( \frac { x } { b } \right) , a b$ and identify each as a relative maximum, relative minimum, or neither.

Question

Find the critical numbers for $f ( x ) = \tan ^ { - 1 } \left( \frac { x } { a } \right) - \tan ^ { - 1 } \left( \frac { x } { b } \right) , a > b$ and identify each as a relative maximum, relative minimum, or neither.

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The Answer of Find the critical numbers for $f ( x ) = \tan ^ { - 1 } \left( \frac { x } { a } \right) - \tan ^ { - 1 } \left( \frac { x } { b } \right) , a > b$ and identify each as a relative maximum, relative minimum, or neither.

Find the Critical Numbers For f(x)=tan⁡−1(xa)−tan⁡−1(xb),a>bf ( x ) = \tan ^ { - 1 } \left( \frac { x } { a } \right) - \tan ^ { - 1 } \left( \frac { x } { b } \right) , a > bf(x)=tan−1(ax​)−tan−1(bx​),a>b

Find the Critical Numbers For $f ( x ) = \tan ^ { - 1 } \left( \frac { x } { a } \right) - \tan ^ { - 1 } \left( \frac { x } { b } \right) , a > b$