Name the Curve Before You Read It

You'll learnhow a feature of f shows up on the graph of f′ and again on the graph of f″, how to build a sketch from those two graphs, and which questions a graph of f′ cannot answer.

One function, drawn three times: itself, its slope, and the slope of its slope. Where the top curve turns around, the middle curve crosses the axis, and where the middle curve turns around, the bottom one crosses. Learn that shift and you can sketch f from a graph of f′, sort three unlabelled curves, and dodge the trap of reading a peak off the wrong curve. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · A TURNING POINT ON ONE CURVE IS A CROSSING ON THE NEXT · v2

f turns ⇒ f′ crosses · f′ turns ⇒ f″ crosses · say which curve it is before you read it

Before you start

What you're looking at

One function drawn three times on a shared x axis: itself on top, its slope in the middle, the slope of its slope underneath.

The question

When the top curve turns around, what happens on the curves below it?

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