Question

Consider f(x)=x(x^3+1)+6x^2-8xDescribe the end behavior of f how do you know?

Answer 1

first, we note that if x is positive, then f(x) is positive only if x(x^3+1)+6x^2-8x, that is, if x is >1,

if x=0, then f(0)=0 and 0 is a root,

if x=1, then f(1)=0 and 1 is a root.

There are no other roots, and

f(x)>0 if x>1 or x<0, and f(x)<0 if 0

Now we wil graph the function (note that it goes up as x is bigger! and as x is smaller!