Differential And Integral Calculus By Feliciano And Uy Chapter 10 [ SECURE ]

For current students facing Chapter 10 for the first time: the frustration is real, but so is the triumph. The chapter’s exercises are not busywork; they are mental push-ups. And when you finally solve that related rates problem — the one with the rotating lighthouse and the moving ship — you will have earned not just a correct answer, but a new way of seeing change itself.

Another strength is the chapter’s . Early exercises are straightforward: find the slope of the tangent to $y = x^3 - 3x$ at $x=2$. By the end of the problem set, students face multi-step optimization puzzles involving costs, revenues, and geometric constraints that mimic real engineering design challenges. The Infamous “Feliciano and Uy” Problem Sets Ask any Filipino engineer over 40 about Chapter 10, and they will likely grimace with a fond nostalgia. The unsolved exercises at the back of each subsection are legendary — not because they are impossible, but because they require translation from English to mathematics. Consider this classic optimization problem (paraphrased from memory of the 1980s edition): “A rectangular sheet of tin 12 inches by 8 inches has four equal squares cut from each corner. The flaps are then folded up to form an open box. Find the size of the square to be cut out so that the volume of the box is maximum.” The solution requires defining $x$ as the side of the square, expressing volume $V(x) = (12-2x)(8-2x)x$, differentiating, setting $V'(x)=0$, and checking the second derivative. Simple enough — but Feliciano and Uy often add a twist: “If the tin costs PhP 0.50 per square inch and the box is to be sold for PhP 15.00, is it profitable?” Suddenly, it’s not just calculus; it’s economics. For current students facing Chapter 10 for the

Moreover, the chapter introduces — problem-solving strategies. For optimization, students are taught: 1) Draw a diagram. 2) Identify the quantity to be optimized. 3) Express it in terms of one variable. 4) Differentiate. 5) Test critical points. This recipe-like clarity is comforting to students who find pure mathematics intimidating. Another strength is the chapter’s