Question

What s the end behavior of `f(x)=-x^4+2x^2+2x`?

Answer 1

As `x to +- oo, y to - oo`, There is one turning point in `Q_1`, wherein f is the maximum. There are two points of inflexion, at
`x = +-1/sqrt 3`. The graph depicts all these aspects.

Explanation:

`f = -x^4(1-2/x$2-2/x^4) to -oo`, as `x to +-oo`.

f = 0, when x = 0 and also for another `x in (1,2)`,

using `f(1)f(2)<0`.

Likewise, f' = 0, for some `x in (1, 2)`.

f'' = -12x^2+4 = 0, when x = +-1/sqrt 3#, with f''' not 0. So, there are

two ( tangent crossing curve ) points of inflexion, at `x = +-1/sqrt3` . .

graph{y+x^4-2x^2-2x=0 [-10, 10, -5, 5]}