The Second Pass Is a Full Pass

You'll learnwhy a second derivative needs every rule the first one did, how to finish an implicit one, and how to catch a wrong f′′ by the shape of the curve.

A second derivative is the derivative of the first derivative, and f′ is a function like any other: whatever rules it needs, it needs again. The trap is treating the second pass as the easier one. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · f′′ IS THE SLOPE OF f′ · ONE INNER FACTOR PER PASS · v2

f′′ = (f′)′ · every rule, a second time · one inner factor per pass

Before you start

What you're looking at

A function on top and its derivative underneath, on one shared x axis, with a point about to ride across both.

The question

What does the second pass owe you, and what does the picture look like when that debt goes unpaid?

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