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We have seen that the concepts of the convexity and the concavity of a function play an important role in determining sufficient conditions for the existence of local extrema of functions of one variable. The same is true for functions of several variables. Therefore, in this chapter we generalize these concepts to the case of functions of n variables \(y=f(x_{1}, x_{2}\ldots ,x_{n})\) . Furthermore, we derive their characterization using differential calculus.

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Convex and Concave Functions

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  • 发表日期：

    2026年

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  • Zrinka Lukač

摘要

We have seen that the concepts of the convexity and the concavity of a function play an important role in determining sufficient conditions for the existence of local extrema of functions of one variable. The same is true for functions of several variables. Therefore, in this chapter we generalize these concepts to the case of functions of n variables \(y=f(x_{1}, x_{2}\ldots ,x_{n})\) . Furthermore, we derive their characterization using differential calculus.