Răspuns:
f(x)=2x³
Domeniul de definitie R.Codomeniul R
Limite
[tex]\lim_{x \to \infty} 2x^3=[/tex]2*∞³=+∞
[tex]\lim_{ \to- \infty} 2x^3 =[/tex]2*(-∞)³=2*(-∞)=-∞
Asimptote -nu exista
Monotonia
Se calculeaza f `(x)
f `(x)=2*3x²=6x²≥0 Functia e crescatoare
punct de maxim
f `(x)=0 6x²=0 =>x=0
Functia f`(x)>0 pt x<o .de asemenea f `(x)>0 pt x>0=.>
x=0 punct de inflexiune
Derivata 2 f ``(x)=12x Pt x<0 f ``(x)<0 => f concava,Pt x>0 f ``(x)>0 =>
f convexa
Tabel de variatie
x l-∞ 0 +∞
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f `(x)l+ + + + 0 + + + + + +
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f(x) l-∞ / / / / / 0// /// / / / / /
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f ``(x)l - - - - - - 0+++++++++++++++++++++++++++++++++++++++++
∩ U
Atasament
Explicație pas cu pas:
