Practice question · Fill in the blanks
Complete the definition of an inflection point.
An inflection point is a point where ______.
Word bank: the first derivative is zero · the second derivative changes sign · the function value is zero · the function reaches its maximum
Hints
- Inflection is about the bending of the curve, not its height or its slope.
- It is the moment concave up becomes concave down or the reverse.
Show the answer
An inflection point is a point where the second derivative changes sign.
Why
An inflection point is where the concavity flips, which is exactly a sign change in f''. The first derivative may or may not be zero there, for x^3 it is, but for many curves an inflection occurs on a perfectly steep stretch.
Practise Applications of Derivatives
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