a)f `(x)=[x `*(x^4+3)-x*(x^4+3)`]/(x^4+1)^2=(x^4+3)-x*4x^3]/(x^4+3)^2=
(x^4+3-4x^4)/(x^4+3)²=
(x^4+3-4x^4)/(x^4+3)²=(-3x^4+3)/(x^4+3)²=-3(x^4-3)/(x^4+3)²
f `(x) ≤0 =>f(x) strict descrescatoare
b) pt x∈[1,∞)
x=1 f(1)=1/4 x→∞ f(x)=0 =>f([1,∞))=(0,1/4]
x∈[0,1) f(0)=0 x→1 f(x)→1/4
f([0,1))=[0,1/4)
x∈[-1,0) f(-1)=-1/4
f(0)=0 functia fiind strict descrescatoare rezulta f([-1 ,0)=(-1/4 0)
x∈(-∞, -1) x→-1 f(x)→0 x=-1 f(-1)=-1/4
Imf=(0,1/4]U([0,1/4)U(-1/4,0)U(0,-1/4)=[-1/4 ,1/4]
la c ma mai gandesc
