Question

Let f(x)=x^4+2x^3-7x^2-8x+12.

A.) Discuss the short run behavior of
f(x).

B.) Discuss the long run behavior of
f(x).

Answer 1

A) When x = 0, f(x) = 12.
The function probably crosses the x axis a few times. It is 0 when x = 1
B) As x -> + or minus infinity, f(x) goes to infinity and becomes more symmetrical about the y axis, dominated by the x^4 term.