Differential And Integral Calculus By Feliciano And Uy Chapter 4 May 2026
A distinguishing feature of Feliciano and Uy’s text is the rigorous focus on "Theorems and Proofs." Unlike texts that focus purely on application, this chapter often provides the formal proof for the Sum/Difference rules using the limit definition of the derivative.
Furthermore, the problem sets typically progress from simple drill exercises (e.g., "Differentiate $x^10$") to more complex word problems requiring the synthesis of multiple rules (e.g., "Find the slope of the tangent line to $y = (3x^2 - 1)^4$").
In the study of calculus, the derivative represents the instantaneous rate of change of a function. While the definition of the derivative—derived from the concept of limits—is foundational, it is computationally cumbersome for complex functions. Feliciano and Uy dedicate Chapter 4 to streamlining this process. The chapter introduces a set of algebraic rules that allow for the differentiation of functions without resorting to the lengthy process of evaluating limits of difference quotients. Mastery of these rules is prerequisite for applications such as curve sketching, optimization, and related rates found in subsequent chapters. A distinguishing feature of Feliciano and Uy’s text
To determine if a critical point is a max or a min, analyze the sign of the derivative $f'(x)$ around the critical number $c$:
If you want, I can convert this into a social-media-sized caption, a longer study guide with worked problems from Chapter 4, or a printable one-page summary. If you want, I can convert this into
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This is a custom study and solution guide for Chapter 4: Applications of Differential Calculus (commonly titled Applications of the First Derivative) in the textbook Differential and Integral Calculus by Feliciano and Uy (a standard reference in Philippine engineering and math curricula). Keep this list handy while working through Feliciano
Since I do not have the exact 1983/1998 edition text, this guide is reconstructed based on the standard content of Chapter 4 in that specific book, covering: Tangents and Normals, Increasing/Decreasing Functions, Maxima/Minima, Concavity, Points of Inflection, and Applied Optimization.
Keep this list handy while working through Feliciano and Uy Chapter 4:
Having established the fundamental rules of differentiation in previous chapters, Chapter 4 focuses on the utility of the derivative. The derivative is no longer just a mathematical operation; it becomes a tool for analyzing the behavior of functions, determining rates of change, and solving optimization problems.
This chapter generally covers four major topics: Extreme Values of Functions, The Mean Value Theorem, Curve Sketching, and Optimization Problems.