One Number Settles It, Unless It Is Zero

You'll learnhow one value of the second derivative tells a hilltop from a valley floor, and what to do when that value comes out zero.

A curve with two flat spots. One is the top of a hill and one is the bottom of a bowl, and a single number tells them apart. But the same number can also come back zero, and then it has told you nothing at all. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · READ THE SIGN OF f″ · ZERO IS A REFUSAL, NOT A VERDICT · v2

flat tangent · f″ < 0 hilltop · f″ > 0 valley floor · f″ = 0 no answer

Before you start

What you're looking at

A curve with two flat spots, where the tangent line is horizontal. Pink marks are the verdicts.

The question

Which flat spot is a hilltop, which is a valley floor, and how can one number tell?

Step 1 / 12