Consider vectors $\vec{a}$ and $\vec{b}$ on the coordinate plane satisfying $|\vec{a}| + |\vec{b}| = 9$ and $|\vec{a} - \vec{b}| = 7$. Let $|\vec{a}| = x$, where $1 < x < 8$, and let the angle between $\vec{a}$ and $\vec{b}$ be $\theta$. Using the triangle formed by vectors $\vec{a}$, $\vec{b}$, and $\vec{a} - \vec{b}$, we can express $\cos\theta$ in terms of $x$ as $f(x) = \frac{c}{9x - x^2} + d$, where $c$ and $d$ are constants with $c > 0$, with domain $\{x \mid 1 < x < 8\}$. Explain where $f(x)$ is increasing and decreasing in its domain. Determine the value of $x$ for which the angle $\theta$ between $\vec{a}$ and $\vec{b}$ is maximum. (Non-multiple choice question, 4 points)