Question

Va rog, explicati-mi pasii rezolvarii acestui exercitiu (din poza).

Answer 1

[tex]1)aflam f'(x)= \frac{x'* \sqrt{x^2+2x+2}-x*( \sqrt{x^2+2x+2})' }{2 \sqrt{x^2+2x+2} }= \\ = \frac{ \sqrt{x^2+2x+2}-x \frac{2x+2}{2 \sqrt{x^2+2x+2} } }{2 \sqrt{x^2+2x+2} } = \frac{2(x^2+2x+2)-2 x^{2} -2x}{2( x^{2} +2x+2)} = \frac{2x+4}{2( x^{2} +2x+2)}= \\ = \frac{2(x+2)}{2( x^{2} +2x+2)}= \frac{x+2}{ x^{2} +2x+2} \\ rezolvam -ecuatia :f'(x)=0 \\ x+2=0 \\ x=-2 \\ 3)determinam -pe-fiecare din-intervale-semnul -derivatei \\ (-infint;-2)------------------------ \\ pe(-2;+infinit)++++++++++++++++++++++ [/tex]
$4)(-infinit;-2)monoton -descrescatoare \\ (-2;+infinit)-monoton crescatoare$