Exercise 10

Let $p(z)$ be given by the rule $$\begin{gathered} p(z) = \frac{z\tan(z)}{z^2\sec(z) + 1} + 3 e^z + 1 \end{gathered}$$.

1. Determine $p'(z)$.

2. Find an equation for the tangent line to $p$ at the point where $z = 0$.

3. At $z = 0$, is $p$ increasing, decreasing, or neither? Why?