MykolasD (+2617)
Užrašykite [tex]\small trečiojo[/tex] laipsnio funkciją [tex]\small g\left ( x \right ),[/tex] kai [tex]\small g\left ( 0 \right )= g{}'\left ( 0 \right )= \left ( g{}'\left ( 0 \right ){} \right ){}'= 0[/tex] ir[tex]\small g\left ( x \right )= g{}'\left ( x \right )\cdot \left ( g{}'\left ( x \right ) \right ){}'[/tex]
MykolasD (+2617)
Funkcija [tex]\small g\left ( x \right )= ax^{3}+bx^{2}+cx+d[/tex] [tex]\small g\left ( 0 \right )= 0\Rightarrow[/tex][tex]\small g\left ( x \right )= ax^{3}+bx^{2}+cx[/tex] [tex]\small g{}'\left ( x \right )= 3ax^{2}+2bx+c[/tex]
[tex]\small g{}'\left ( 0 \right )= c= 0[/tex] [tex]\small \Rightarrow g\left ( x \right )= ax^{3}+bx^{2}[/tex] [tex]\small \left ( g{}'\left ( 0 \right ) \right ){}'= b= 0[/tex] [tex]\small \Rightarrow[/tex] [tex]\small g\left ( x \right )= ax^{3}[/tex] [tex]\small g{}'\left ( x \right )=3ax^{2}[/tex] [tex]\small \left ( g{}'\left ( x \right ) \right ){}'= 6ax[/tex]
[tex]\small ax^{3}= 3ax^{2}\cdot 6ax[/tex] [tex]\small \Rightarrow[/tex] [tex]\small x^{3}= 18ax^{3}[/tex] [tex]\small \Rightarrow[/tex][tex]\small 18a= 1[/tex] [tex]\small \Rightarrow[/tex][tex]\small a= \frac{1}{18}[/tex] [tex]\small \Rightarrow[/tex][tex][/tex][tex]\small g\left ( x \right )= \frac{1}{18}x^{3}.[/tex]