Chapter 12
Your Problems Are Solved: Differentiation to the Rescue!
IN THIS CHAPTER
Getting the most bang for your buck — optimization problems
Getting up to speed with position, velocity, and acceleration
Related rates — brace yourself
In Chapter 1, I argue that calculus has changed the world in countless ways, that its impact is not limited to Ivory Tower mathematics, but is all around us in down-to-earth things like microwave ovens, cellphones, and cars. Well, it’s now Chapter 12, and I’m finally ready to show you how to use calculus to solve some practical problems.
Getting the Most (or Least) Out of Life: Optimization Problems
One of the most practical uses of differentiation is finding the maximum or minimum value of a real-world function: the maximum output of a factory, the maximum strength of a beam, the minimum cost of running some business, the maximum range of a missile, and so on. Let’s see how this works by walking through some problems.
The maximum volume of a box
A box with no top is to be manufactured from a 30-inch-by-30-inch piece of cardboard by cutting and folding it, as shown in Figure 12-1.
FIGURE 12-1: The box is made from a 30”-by-30” piece of cardboard ...
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