How do you describe the end behavior of y=-x^6+x^4-5x^2+4?

Dec 7, 2016

See explanation and graph.

Explanation:

$y \left(0\right) y \left(\pm 1\right) < 0 \to$ zeros $x \in \left(0 , 1\right) \mathmr{and} \left(- 1 , 0\right)$. Graph reveals proximity to

$\pm 1$.

$y = - {x}^{6}$( 1 + negative powers of x ) $\to - \infty$, as $x \to \pm \infty$.

At x = 0, y'=0 and y''< 0. So, y(0) = 4 is the maximum y.

graph{y+x^6-x^4+5x^2-4=0x^2 [-10, 10, -5, 5]}