Applications of Derivatives · Curve Analysis
Concavity
The second derivative determines concavity. Concave up means the curve opens upward (bowl shape). Concave down means it opens downward.
- 0 variables
- 2 worked examples
- 15 in Applications of Derivatives
Worked examples
Determine the concavity of f(x) = x³ on (-∞, 0) and (0, ∞).
- f''(x) = 6x
- x < 0: f''(x) < 0 → concave down
- x > 0: f''(x) > 0 → concave up
Answer: Concave down on (-∞, 0), concave up on (0, ∞).
1 more worked examplePremium
Find where f(x) = x⁴ - 6x² is concave up and concave down.
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Practice
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