Question

Hello! High school student in Calculus here. I need help solving the problem attached in the image. I'd like help FINDING THE SLOPE at point (pi/2, 0) according to the function:g(x) = cot x. I would greatly appreciate it, thank you! :)))

Answer 1

Given the function:

`g(x)=\cot x`

we know that the derivative of g(x) is:

`g^(\prime)(x)=-\csc ^2x`

then, the slope at point (pi/2,0) is:

`\begin{gathered} g^(\prime)((\pi)/(2))=-\csc ^2((\pi)/(2))=-(1)/(\cos ^2(\pi))=-(1)/((-1)^2)=-(1)/(1)=-1 \\ \Rightarrow g^(\prime)((\pi)/(2))=-1 \end{gathered}`

therefore, the slope is g'(pi/2) = -1