A rectangular sheet of paper 24 cm × 9 cm is to be made into a box with an open top by cutting equal squares from the corners and folding up the sides. Find the side of the square to be cut so that the volume is maximum.

Do not treat Differential and Integral Calculus by Feliciano and Uy as a novel. Treat it as a workbook. Write in the margins. Erase and redo problems. Chapter 4 is difficult, but it is also beautiful. Master it, and the rest of calculus (integration, differential equations) becomes a much friendlier journey.

A 5m ladder slides down a wall. Top slides down at 1 m/s. How fast is bottom moving when top is 3m from ground? (x^2 + y^2 = 25), (\fracdydt = -1), find (\fracdxdt) when (y=3). → (x=4), (2x\fracdxdt + 2y\fracdydt = 0) → (8\fracdxdt + 6(-1)=0) → (\fracdxdt = 0.75) m/s.

Feliciano and Uy then discuss the applications of maxima and minima in various fields, including: