In many .zip files, this problem is solved in two lines, missing the nuance. A better solution manual would include a diagram and a note about why ( \theta'(s) ) fails at inflection points.
Occasionally, out-of-print instructor supplements appear here. Look for "Instructor's Manual" alongside the .zip keyword. Unlocking Curves and Surfaces: A Complete Guide to
The "do Carmo Differential Geometry of Curves and Surfaces Solution Manual.zip" is crucial for: Unlocking Curves and Surfaces: A Complete Guide to
Some professors publish their solutions for enrolled students. Search: "Differential Geometry" "Do Carmo" solutions site:.edu Unlocking Curves and Surfaces: A Complete Guide to