Given the function:
[tex]g(x)=\cot x[/tex]
we know that the derivative of g(x) is:
[tex]g^{\prime}(x)=-\csc ^2x[/tex]
then, the slope at point (pi/2,0) is:
[tex]\begin{gathered} g^{\prime}(\frac{\pi}{2})=-\csc ^2(\frac{\pi}{2})=-\frac{1}{\cos ^2(\pi)}=-\frac{1}{(-1)^2}=-\frac{1}{1}=-1 \\ \Rightarrow g^{\prime}(\frac{\pi}{2})=-1 \end{gathered}[/tex]
therefore, the slope is g'(pi/2) = -1
