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Functions › Functional equations › Extremes in functional equations

Maximum of a piecewise function

High school · ●●○○○ 20 pts

Define a new operation ⊕\oplus as follows: when a≥ba \geq b, a⊕b=aa \oplus b = a; when a<ba < b, a⊕b=b2a \oplus b = b^2. Let f(x)=(1⊕x)⋅x−(2⊕x)f(x) = (1 \oplus x)\cdot x - (2 \oplus x) for x∈[−2,2]x \in [-2, 2]. Find the maximum value of f(x)f(x).

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piecewise functionsoptimizationcustom operations