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

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Answer 1 · 2016-12-07T07:20:08

See explanation and graph.

$y (0) y (\pm 1) < 0 \to$ $y(0)y(+-1)<0 to$ zeros $x \in (0, 1) and (- 1, 0)$ $x in (0, 1 )and (-1, 0)$ . Graph reveals proximity to

$\pm 1$ $+-1$ .

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

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]}

How do you describe the end behavior of y=-x^6+x^4-5x^2+4y=−x6+x4−5x2+4y=-x^6+x^4-5x^2+4?