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Let $f(x)$ be: $f(x) = \begin{cases} \dfrac{(1-x) (t-x (t-2))^2}{16 (x (2 e-1)+1)} & in\,\, \mathcal{R} \\[6pt] \text{Indeterminate} & \text{Otherwise} \end{cases} $

Where $$\mathcal{R} = \biggl\{ (t,e,x) \mid (t \geq 2 \land \frac{1}{2} < e \leq 1 \land z < x < 1) \lor (1 \leq t < 2 \land 0 \leq e < \frac{1}{2} \land 0 \leq x < z) $$ $$ \lor (1 \leq t \leq 2 \land \frac{1}{2} \leq e \leq 1 \land 0 \leq x < 1) \biggr\}$$

and $ z = \frac{t-2}{4 e+t-4}$

How shall I go to solve the problem: $$ \max_{x} f(x) \text{ s.t. } 0 \leq x \leq 1 $$

Shall I just maximize with KKT as if the function was only $\dfrac{(1-x) (t-x (t-2))^2}{16 (x (2 e-1)+1)}$ and then discard anything that is not inside $\mathcal{R}$?

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