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

1 Answer
Aug 7, 2016

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