Question 1155524
As x increases without bound + it goes to +oo
as x increases negatively without bound, it goes to - oo, because it has an odd exponent in the first term.

First derivative is x^4+4x^3-12x^2
set that equal to 0 and factor out a x^2 to get x^2(x^2+4x-12)=0
=x^2(x+6)(x-2)=0, Critical points are (-6, 0, 2)

{{{graph(300,300,-25,5,-100,1000,(1/5)x^5+x^4-4x^3+3)}}}
{{{graph(300,300,-3,4,-20,20,(1/5)x^5+x^4-4x^3+3)}}}

Those are the x-values; substitute into the original function to get the y-values.