Question

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

Answer 1

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

Explanation:

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`