Consider the function \( f(x)=\max \left\{x^{2}\right. \),
\[
\left.(1-x)^{2}, 2 x(1-x)\right\},...
Consider the function \( f(x)=\max \left\{x^{2}\right. \),
\[
\left.(1-x)^{2}, 2 x(1-x)\right\}, x \in[0,1]
\]
The interval in which \( f(x) \) is increasing, is
(a) \( \left(\frac{1}{3}, \frac{2}{3}\right) \)
(b) \( \left(\frac{1}{3}, \frac{1}{2}\right) \)
(c) \( \left(\frac{1}{3}, \frac{1}{2}\right) \cup\left(\frac{1}{2}, \frac{2}{3}\right) \)
(d) \( \left(\frac{1}{3}, \frac{1}{2}\right) \cup\left(\frac{2}{3}, 1\right) \)
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