Răspuns:f
Explicație pas cu pas:
f(x)=x⁶
Domeniul de definitie R
INtersectia cu axele
f(0)=0⁶=0
O(0,0)
LIitele la capete
x-> -oolim f(x)=-oo⁶=+oo
x->+oo limf(x)=+oo⁶=+oo
DErivata 1
f `(x)=6x⁵
Monotononia
Pt x<0 f `(x) <0 => f desccrescatoare
x>0 f `(x)=6x⁵>0=> f cescatoare
Punct de extrem\
f `(x)=0 6x⁵=0=>
x=0 Punct de extrem .Deoarece f `(x)<0 ;la stanga lui0 si f `(x)>0 la dreapta lui 0=> o este punctde minim
Derivata 2 f ``(x)=(6x⁵) `=6*5x⁴=30x⁴≥0=> f convexa pe D
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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l+ ++ +++++++ +++ ++
f ``(x) l∪ ∪∪ ∪∪ ∪∪∪ ∪∪∪ ∪∪
