Practice question · Put in order
Order the curve-sketching checklist.
- Use the sign of f' to find where the curve rises and falls and to locate the critical points
- Find the vertical and horizontal asymptotes
- Use the sign of f'' to find the concavity and the inflection points
- Assemble all the features into a sketch
- Find the domain and the intercepts
Hints
- The cheapest information, where the function exists and where it meets the axes, comes first.
- Bending refines the rising-and-falling skeleton, so it comes after it.
Show the answer
- Find the domain and the intercepts
- Find the vertical and horizontal asymptotes
- Use the sign of f' to find where the curve rises and falls and to locate the critical points
- Use the sign of f'' to find the concavity and the inflection points
- Assemble all the features into a sketch
Why
The order moves from position to slope to bending: intercepts and asymptotes fix where the curve is, f' gives the up-and-down skeleton, and f'' supplies the shape between the turning points. Sketching from f' alone gets the direction right and the shape wrong.
Practise Curve Sketching
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