How do you graph $f (x) = x^{3} - 12 x^{2} + 45 x - 54$ $f(x)=x^3-12x^2+45x-54$ and identify domain, range, max, min, end behavior, zeros?

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Answer 1 · 2016-12-07T01:40:43

See explanation.

$y = f (x) = x^{3} - 12 x^{2} + 45 x - 54$ $y =f(x)=x^3-12x^2+45x-54$ , with a zero x = 3.

$y'=3x^2-24x+45$ , with zeros x = 3 and 5.

x = 3 is a double root. So, the third root is 9.

y'' = 6x - 24 = 0, at x = 4, < 0 at x = 3 and > 0 at x = 5..

y'''= 6.

Maximum y = y(3) = 0.

Minimum y = y(5) = $- 4$ .

Point of inflexion: (4. -2).

$y = x^3(112/x+45/x^2-64/x^3) to +-oo$ , as $x to +-oo$ .

Domain and range: $(- oo, oo)$

graph{x^3-12x^2+45x-54 [-10, 10, -5, 5]}

How do you graph f(x)=x^3-12x^2+45x-54f(x)=x3−12x2+45x−54f(x)=x^3-12x^2+45x-54 and identify domain, range, max, min, end behavior, zeros?