Is $f(x)=(x^3-9x^2+12x+2)/(x+1)$ increasing or decreasing at $x=0$ ?

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Answer 1 · 2016-09-02T05:45:32

$f(x)$ is increasing at $x=0$

Given -

$y=(x^3-9x^2+12x+2)/(x+1)$

$dy/dx={[(x+1)(3x^2-18x+12)]-[(x^3-9x^2+12x+2)(1)]}/(x+1)^2$

At $x=0$

$dy/dx={[(0+1)(3(0)^2-18(0)+12)]-[((0)^3-9(0)^2+12(0)+2)(1)]}/(0+1)^2$

$dy/dx=(12-2)/1=10>1$

$f(x)$ is increasing at $x=0$

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Is f(x)=(x^3-9x^2+12x+2)/(x+1)f(x)=(x^3-9x^2+12x+2)/(x+1) increasing or decreasing at x=0x=0?