Practice question · Put in order
Order the steps of locating the inflection points of a twice-differentiable function.
- Solve f'' (x) = 0 and note any points where f'' is undefined
- Test the sign of f'' on each side of every candidate
- Compute the second derivative
- Keep only the candidates where the sign actually changes
Hints
- Solving f'' = 0 produces candidates, not answers.
- The final filtering step is the one that distinguishes x cubed from x to the fourth.
Show the answer
- Compute the second derivative
- Solve f'' (x) = 0 and note any points where f'' is undefined
- Test the sign of f'' on each side of every candidate
- Keep only the candidates where the sign actually changes
Why
The last two steps are the ones that get skipped, and skipping them wrongly promotes x = 0 on the graph of x to the fourth. Candidates must be filtered by an actual sign change, which is the definition of an inflection point.
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