Check if f(x) < 0 (strictly concave) for common functions
Select Function
f(x)=x^2+x+
f(x)=ln(x) (domain x>0)
f(x)=x+
f(x)=-e^(x)
Result
Derivation
Strict Concavity
f(x) < 0: STRICTLY CONCAVE
f(x) <= 0: concave (not strictly)
f(x) > 0: convex (not concave)
Unique global maximum guaranteed
Strict concavity requires f(x) < 0 at every point. This ensures a unique global maximum. Linear functions (f=0) are concave but not strictly concave. Strict concavity is a stronger condition used in optimization and economic theory.
⚠Strictly concave requires f(x) < 0 everywhere. Linear functions (f=0) are concave but NOT strictly concave.
What Is Strict Concavity?
Strict concavity is stronger than concavity. It requires f(x) < 0 at every point. Strictly concave functions have a unique global maximum with no flat sections. They are the opposite of strictly convex functions and are important in utility theory and risk analysis.
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