Chapter 12 - Vector-Valued Functions - 12.3 Change Of Parameter; Arc Length - Exercises Set 12.3 - Page 867: 40

\(t = g(\tau) = 1 - \tau\)

Step 1 Let \(g\) be a decreasing function and so \(t = g(\tau)\) gives that \(t\) decreases when \(\tau\) increases, and the graph of \(r(t)\) is traced in the opposite direction as \(\tau\) increases. We will choose \(g\) as a linear function, such that \(t = g(\tau) = 1 - \tau\) Result \(t = g(\tau) = 1 - \tau\)