Is $f (x) = \frac{x^{3} - 4 x^{2} - 2 x - 4}{x - 1}$ $f(x)=(x^3-4x^2-2x-4)/(x-1)$ increasing or decreasing at $x = 2$ $x=2$ ?

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Is $f (x) = \frac{x^{3} - 4 x^{2} - 2 x - 4}{x - 1}$ $f(x)=(x^3-4x^2-2x-4)/(x-1)$ increasing or decreasing at $x = 2$ $x=2$ ?

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Answer 1 · 2016-04-12T06:02:08

Increasing.

Explanation:

Express the ratio in the quotient remainder form
$x^{2} - 3 x - 5 - \frac{9}{x - 1}$ $x^2-3x-5-9/(x-1)$
$f' = 2x-3 + 9/(x-1)^2$ .
At x = 2, f' = 10 > 0.
So, f is increasing at x = 2.

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Is $f (x) = \frac{x^{3} - 4 x^{2} - 2 x - 4}{x - 1}$ $f(x)=(x^3-4x^2-2x-4)/(x-1)$ increasing or decreasing at $x = 2$ $x=2$ ?

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Is f(x)=(x^3-4x^2-2x-4)/(x-1)f(x)=x3−4x2−2x−4x−1f(x)=(x^3-4x^2-2x-4)/(x-1) increasing or decreasing at x=2x=2x=2?

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Explanation:

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Is $f (x) = \frac{x^{3} - 4 x^{2} - 2 x - 4}{x - 1}$ $f(x)=(x^3-4x^2-2x-4)/(x-1)$ increasing or decreasing at $x = 2$ $x=2$ ?