Помогите решить,пожалуйста

Решите задачу:

$y=\sqrt{3x^2+5}-\sqrt{3x^2}\; ,\; \; x\in [\, 0;3\, ]\\\\y'= \frac{6x}{2\sqrt{3x^2+5}} - \frac{6x}{\sqrt{3x^2}}= \frac{x\cdot \sqrt{3x^2}-x\cdot \sqrt{3x^2+5}}{\sqrt{3x^2}\cdot \sqrt{3x^2+5}} = \frac{x\cdot (\sqrt{3x^2}-\sqrt{3^2+5})}{\sqrt{3x^2(3x^2+5)}} =\\\\= \frac{x\cdot (\sqrt{3x^2}-\sqrt{3x^2+5})}{|x|\cdot \sqrt{3(3x^2+5)}} =[\, |x|=x\; pri\; x\in [\, 0,3\, ]\; ]= \frac{\sqrt{3x^2}-\sqrt{3x^2+5}}{\sqrt{3\cdot (3x^2+5)}} =0$

$\sqrt{3x^2}=\sqrt{3x^2+5}\\\\3x^2=3x^2+5\; \; \Rightarrow \; \; 0=5\; neverno$

$x\in \varnothing \\\\y(0)=\sqrt5\approx 2,24\\\\y(3)=\sqrt{32}-\sqrt{27}\approx 0,46\\\\y_{naimen}=\sqrt{32}-\sqrt{27}$