0\\\\Znaki\; y'\; :\; \; (0)+++(\frac{1}{\sqrt2})---(1)\\\\x=\frac{1}{\sqrt2}=x_{max}" alt="y=x+\sqrt{1-x^2}\; ,\\\\ ODZ:\; \; 1-x^2 \geq 0,\; x^2-1 \leq 0,\; (x-1)(x+1) \leq 0\\\\x\in [\, -1;1\, ]\\\\y'=1+\frac{-2x}{2\sqrt{1-x^2} }=1-\frac{x}{\sqrt{1-x^2}}=0\\\\\frac{x}{\sqrt{1-x^2}}=1\; ,\; x=\sqrt{1-x^2}\geq 0\; \to \; 1-x^2=x^2\; ,2x^2=1\; ,\; x^2=\frac{1}{2}\\\\x=\pm \frac{1}{\sqrt2}\, ,x=\frac{1}{\sqrt2}>0\\\\Znaki\; y'\; :\; \; (0)+++(\frac{1}{\sqrt2})---(1)\\\\x=\frac{1}{\sqrt2}=x_{max}" align="absmiddle" class="latex-formula">