Question

Is `f(x)=(2x^3+5x^2-9x+1)/(x-4)` increasing or decreasing at `x=0`?

Answer 1

`uarr`. See the rise, in the graph, at `(0, -1/4)`

Explanation:

graph{(2x^2+13x+43+173/(x-4)-y)(x^2+(y+.25)^2-.01)=0 [-10, 10, -5, 5]}

By actual division,

`f=2x^2+13x+43+173/(x-4)`

`f'=4x+13-173/(x-4)^2=13-173/16=35/16 >0`, at x = 0.

So, `f uarr` as `x uarr`, at `(0,-1/4)`.