Question

Помогите решить,пожалуйста

Answer 1

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

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

$xin varnothing \\y(0)=sqrt5approx 2,24\\y(3)=sqrt{32}-sqrt{27}approx 0,46\\y_{naimen}=sqrt{32}-sqrt{27}$