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

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Answer 1 · 2016-12-07T07:20:08

See explanation and graph.

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

$+-1$ .

$y=-x^6$ ( 1 + negative powers of x ) $to -oo$ , as $x to +-oo$ .

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=-x^6+x^4-5x^2+4?