Question

Is `f(x)=(-2x^2-15x-12)/(2x-4)` increasing or decreasing at `x=0`?

Answer 1

Given -

`y=(-2x^2-15x-12)/(2x-4)`

`dy/dx={[(2x-4)(-4x-15)]-[(-2x^2-15x-12)(2)]}/(2x-4)^2`

`dy/dx={[-8x^2+16x-30x+60]-[-4x^2-30x-24]}/(2x-4)^2`

`dy/dx={[-8x^2-14x+60]-[-4x^2-30x-24]}/(2x-4)^2`

`dy/dx=(-4x^2+16x+84)/(2x-4)^2`

At `x=0`

`dy/dx=(-4(0^2)+16(0)+84)/(2(0)-4)^2=84/16>0`

Since `dy/dx >0` at `x=0`, the function is increasing `x=0`