The exercises at the end of Chapter 4 progress systematically from basic computational exercises (finding slopes) to complex verbal word problems (multi-variable optimization).
Why does this specific textbook chapter generate so many search queries? Because is the filter. In many engineering programs, passing the exam on Chapter 4 of Feliciano and Uy determines whether you proceed to Integral Calculus.
The concepts in Chapter 4 are not isolated; they are the building blocks for what comes next in the Feliciano and Uy textbook. Here's a quick look at where you'll apply these skills in later chapters: The exercises at the end of Chapter 4
Feliciano and Uy are known for providing numerous exercises. The best way to master this chapter is to:
$$V = \frac43\pi r^3$$
In addition to the differentiation of trigonometric functions, the chapter also covers the differentiation of inverse trigonometric functions, including:
Here, the chapter delves into the derivatives of logarithmic and exponential functions. A standout technique introduced is (Section 4.7). This method is a powerful shortcut for finding derivatives of complex functions involving products, quotients, or powers by first taking the natural logarithm of both sides. In many engineering programs, passing the exam on
The authors heavily penalize sloppy notation. Correct usage of differentials (
$$\fracdVdt = \frac43\pi (3r^2) \fracdrdt$$$$\fracdVdt = 4\pi r^2 \fracdrdt$$ The best way to master this chapter is
: Use specific limit theorems to derive transcendental derivatives.
Let $x$ be the width perpendicular to the river, and $y$ be the length parallel to the river. Perimeter constraint: $2x + y = 120 \implies y = 120 - 2x$ Area to maximize: $A = x \cdot y$