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Home  Continuous Functions Derivatives and Curve Sketching Theorem 2: Graphical Meaning of the Second Derivative |
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Theorem 2: Graphical Meaning of the Second Derivative
The next theorem gives the geometric meaning of the sign of the second derivative. THEOREM 2 Suppose f is continuous on I and f has a second derivative at every interior point of I. (i) If f"(x) > 0 for all interior points x of I, then f is concave upward on I. (ii) If f"(x) < 0 for all interior points x of I, then f is concave downward on I. We have already explained the intuitive reason for Theorem 2. The proof is omitted.
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Last Update: 2006-11-05