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A^{\prime}(x)=4\left[\frac{-x^{2}}{\sqrt{1-x^{2}}}+\sqrt{1-x^{2}}\right]=4 \frac{1-2 x^{2}}{\sqrt{1-x^{2}}} \begin{cases} > 0 & \text { if } 0 < x < 1 / \sqrt{2} \\ < 0 & \text { if } 1 / \sqrt{2} < x < 1\end{cases}