Two Equations In, One Function Out

You'll learnhow to turn a word problem into one function of one variable on a stated domain, which is everything that has to happen before a derivative can be taken.

A farmer has 1200 feet of fence and a river along one side of the field. Every shape that uses all the fence has a different area, and the question is which shape has the biggest one. Before any calculus can answer that, the problem has to become one function of one variable, with a domain the situation supplies. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · ONE LETTER AND A STATED DOMAIN BEFORE ANY DERIVATIVE · v2

A = xy · 2x + y = 1200 ⇒ A(x) = x(1200 − 2x) on 0 < x < 600

Before you start

What you're looking at

A rectangular field with a river along one side, so only three sides need fencing. There are 1200 feet of fence.

The question

What has to be written down before a derivative can be taken at all?

Step 1 / 12