Balancing $f$ and $g$

★ 6/10functions Extrema Substitution algebra

Problem

Let $f(x) = x$ and $g(x) = x^2 - x + 3$ . Suppose there exist $x_1, x_2, \dots, x_n \in \left[0, \dfrac{9}{2}\right]$ such that

f(x_1) + f(x_2) + \cdots + f(x_{n-1}) + g(x_n) = g(x_1) + g(x_2) + \cdots + g(x_{n-1}) + f(x_n).

Find the maximum possible value of $n$ .

Answer

Solution

Difficulty	6/10
Topics	functions, Extrema, Substitution, algebra

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