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Chapter 27 of 46

The Complete Portrait: f, f′, f″ Together

From a function's derivative alone you can draw its shape blind. The three graphs are one object seen three ways.

Free12–16 min

By the end

Each chapter closes with capabilities, not topics. Watch for these.

01Sketch a function from an analysis of f' and f''
02Move fluently among the graphs of f, f', and f''
03Match features across the three representations