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Calculus · DER

Concavity and Inflection Points — Second Derivative Test

f''(x) > 0 → concave up; f''(x) < 0 → concave down. Inflection points occur where f''(x) changes sign.

CalculusCommon Core FUN-1.CDERVerified correct ✓

Worked examples

Let f(x) = 2x³ - 6x² + 2x + 0. Find f''(x) and determine the x-coordinate of any inflection point. Round to 4 decimal places.
Answer: 1
Let f(x) = 1x³ + 3x² + 4x - 2. Find f''(x) and determine the x-coordinate of any inflection point. Round to 4 decimal places.
Answer: -1

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