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

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Answer 1 · 2016-12-19T02:10:23

See explanatiion

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

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

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

$y''=-6(x-1) =0 at x =1, >0 at x =0 and <0 a tx = 2$

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]}

How do you describe the end behavior for f(x)=-x^3+3x^2-4f(x)=−x3+3x2−4f(x)=-x^3+3x^2-4?