Chapter 5 - Trigonometric Functions - Section 5.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions - 5.5 Assess Your Understanding - Page 442: 44

$\frac{6}{\pi}$.

1. Given $f(x)=sec(2x)$, we have $f(0)=sec(0)=1$ and $f(\frac{\pi}{6})=sec(\frac{\pi}{3})=2$, 2. The rate of change required is given by $\frac{f(\frac{\pi}{6})-f(0)}{\frac{\pi}{6}-0}=\frac{2-1}{\frac{\pi}{6}}=\frac{6}{\pi}$.