Applications of Derivatives · Curve Analysis
Inflection Points
An inflection point is where the concavity changes. Find candidates where f''(x) = 0 or is undefined, then verify concavity changes.
- 0 variables
- 2 worked examples
- 15 in Applications of Derivatives
Worked examples
Find the inflection points of f(x) = x³ - 3x² + 2.
- f'(x) = 3x² - 6x, f''(x) = 6x - 6
- f''(x) = 0 → x = 1
- f''(0) = -6 < 0 (concave down), f''(2) = 6 > 0 (concave up)
- Concavity changes at x = 1 ✓. f(1) = 0.
Answer: Inflection point at (1, 0).
1 more worked examplePremium
Find the inflection point of f(x) = x eˣ.
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