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用多项式函数建模
为什么在涉及盒子、圆柱等三维容器的体积与表面积的问题中，多项式会自然出现？
1. Introduction
Introduction
2. Volume, surface area, and constraints
Volume, surface area, and constraints
3. Other applications of polynomial functions
Other applications of polynomial functions
4. Volume of the folded box
A 12-by-18 inch cardboard has squares of side x cut from each corner and the sides folded up. What are the box's dimensions?
5. Constraint to a single variable
A package's girth plus length must be 120 inches, with girth 4x and length y. Writing y in terms of x gives y = 120 - 4x, so V(x) = x^2(120 - 4x). What is V when x = 5?
6. Contextual domain of a volume function
For V(x) = x^2(120 - 4x), what is the physical domain?
7. Cylinder volume as one variable
A closed cylinder with surface area 60 square inches satisfies h = 30/(pi r) - r, so V(r) = 30r - pi r^3. What is V when r = 1? Round to two decimal places.
8. Taylor approximations to sine
Adding terms to the Taylor polynomials of sine (T1, T3, T5, ...) has what effect on accuracy?
9. A closed box's surface area can be written in one variable
Using the volume constraint to eliminate the height lets a box's surface area or volume be written as a function of one variable.