# How do you describe the end behavior for f(x)=-x^3+3x^2-4?

Dec 19, 2016

See explanatiion

#### Explanation:

$y = - {x}^{3} \left(1 - \frac{3}{x} + \frac{4}{x} ^ 3\right) \to - \infty$, as $x \to \infty \mathmr{and}$

$y \to \infty$, as $x \to - \infty$

$y ' = - 3 x \left(x - 2\right) = 0$, when x = 0 and 2

$y ' ' = - 6 \left(x - 1\right) = 0 a t x = 1 , > 0 a t x = 0 \mathmr{and} < 0 a t x = 2$

Local min y = y(0) = -4, max y = y(x) = 0 and (1, -2) is the point of

inflexion.

graph{-x^3+3x^2-4 [-10, 10, -5, 5]}