A Symmetric Derivative Condition

★ 7/10functions calculus Monotonicity Symmetry

Problem

A function $f(x)$ is differentiable on $\mathbb{R}$ , with

f(-x) + f(x) = x^2 \quad \text{for all } x, \qquad f'(x) > x \quad \text{on } (0, +\infty).

f(2 - a) - f(a) \geqslant 2 - 2a,

find the range of possible values of the real number $a$ .

Answer

Solution

Difficulty	7/10
Topics	functions, calculus, Monotonicity, Symmetry

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