Question

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

Answer 1

decreasing

Explanation:

`d/dx f(x) = ((3x^2-5x-1)*(2x-1) - (2(x^3-5x-x+2)))/(2x-1)^2`

if `x=0`

`d/dx f(0) = (1-2)/(1) = -1`

so it's decreasing on `x=0`

you can even see it on the graph below

graph{(x^3-5x^2-x+2)/(2x-1) [-10, 10, -5, 5]}