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

question 231

Essay

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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Definitions:

Negligently

A rephrased definition: Acting with a lack of proper care or attention that a reasonably prudent person would exercise in similar circumstances.

Negligently

Acting with a lack of proper care or attention, resulting in harm or injury to another person or property.

Relative Capital Contributions

The contributions, often in the form of money or assets, that partners make relative to one another in a partnership or investment setting.

Dissolved

The process of legally disbanding a corporation or partnership, effectively ending its existence.