By systematically working through the exercise sets at the end of Chapter 4, you will build the mathematical intuition necessary to handle the next major phase of the book: Integral Calculus.
Feliciano and Uy emphasize two primary tests to determine if a critical point is a maximum or minimum:
Unlike some modern textbooks that gloss over heavy algebra, Feliciano and Uy require students to maintain meticulous algebraic precision, a skill vital for board exam preparation in engineering. Tips for Mastering Chapter 4 By systematically working through the exercise sets at
This chapter shifts focus from how to find a derivative to why we find it. It teaches students how to use the derivative to analyze the behavior of mathematical curves, solve complex optimizations, and track rates of change across interacting variables. The core themes of Chapter 4 include: Time Rates (Related Rates) Curve Tracing (Extrema and Concavity) Applied Optimization (Maxima and Minima Problems) Key Mathematical Concepts Covered 1. Tangents and Normals to Curves
Chapter 4 typically breaks down into several key areas. Here are the core topics you will find: It teaches students how to use the derivative
Optimization is the process of finding the absolute maximum or minimum value of a function within a specified domain. It answers practical engineering questions like: How do we maximize the volume of a box using a fixed amount of material? or What path minimizes the cost of laying an underwater cable? The Feliciano & Uy Approach to Optimization:
A point where the graph changes its concavity (from concave up to concave down, or vice versa). This occurs where or is undefined, and the sign actually changes. 4. Optimization Problems Here are the core topics you will find:
The authors categorize these into three distinct geometric models: Radical Form Trigonometric Substitution Derived Identity