Answer
The y-intercept is 0
The x-intercepts are 0 and 2
$\lim\limits_{x \to \infty} (2x^3-x^4) = -\infty$
$\lim\limits_{x \to -\infty} (2x^3-x^4) = -\infty$
Work Step by Step
$y = 2x^3-x^4$
When $x=0$, then $~~y = 2(0)^3-(0)^4 = 0$
When $y=0$:
$2x^3-x^4 = 0$
$x^3(2-x) = 0$
$x = 0, 2$
$\lim\limits_{x \to \infty} ( 2x^3-x^4)$
$=\lim\limits_{x \to \infty} x^3(2-x)$
$ = -\infty$
$\lim\limits_{x \to -\infty} (2x^3-x^4)$
$=\lim\limits_{x \to -\infty} x^3(2-x)$
$ = -\infty$
