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Economics 214 Lecture 8 Introduction to Functions Cont.
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Necessary & Sufficient Conditions Symbol means “implies” P Q means “if P then Q,” “P implies Q,” “P only if Q.” P is a sufficient condition for Q, for if P holds then if follows that Q holds. This expression also shows that Q is a necessary condition for P cause P can only hold if Q holds.
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Example of Necessary and Sufficient Conditions f strictly concave f concave
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If and only if
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Power Functions
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Rules of Exponents
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Power functions with p equal even integer F(0)=0 If k>0, then f(x) reaches a global minimum at x=0. If k<0, then f(x) reaches global maximum at x=0. These functions are symmetric about the vertical axis. They are strictly convex if k>0 or strictly concave if k<0.
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Figure 2.13 Power Functions in Which the Exponent Is a Positive Even Number
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