Solve It, Justify It, Then Answer the Question

You'll learnhow to carry a one-variable objective to a defensible answer: differentiate, solve, keep only the roots in the domain, show the survivor is the extremum, and report the quantity that was asked for.

Topic 5.10 turned the fence problem into one function on one domain. This topic runs it to a number, and then does the two things that decide whether the number counts: showing that the critical input really is the maximum, and reporting the quantity the question named rather than the one the equation handed over. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · A CRITICAL INPUT IS NOT YET AN ANSWER · v2

A(x) = x(1200 − 2x) ⇒ A′ = 1200 − 4x ⇒ x = 300, y = 600, A = 180,000 ft²

Before you start

What you're looking at

The area of the three-sided fenced field from 5.10, A(x) = x(1200 − 2x), plotted against the side length x in feet.

The question

Solving A′ = 0 takes one line. What makes the answer worth full marks?

Step 1 / 12