Provide an Appropriate Response $y = 4 \cot \left( \frac { \pi x } { 2 } \right)$

Short Answer

Provide an appropriate response.
-Find the tangent to the curve $y = 4 \cot \left( \frac { \pi x } { 2 } \right)$ at $x = \frac { 1 } { 2 }$ . What is the largest value the slope of the curve can ever have on the interval $- 2 < x < 0$ ?