Question

Is `f(x)=(-2x^3+3x^2+3x-4)/(4x-2)` increasing or decreasing at `x=0`?

Answer 1

`f' (0)=5/2` therefore INCREASING

Positive value indicates INCREASING

Explanation:

`f' (x)=((4x-2)(-6x^2+6x+3)-(-2x^3+3x^2+3x-4)(4))/(4x-2)^2`

`f' (0)=((-2)(3)-(-4)(4))/(-2)^2`

`f' (0)=(-6+16)/4`

`f' (0)=5/2` therefore INCREASING