Question

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

Answer 1

`f(x)={-x^2(x+1)+2(x+1)}/(x+1)=2-x^2`

`:. f'(x)=-2x` graph{2-x^2 [-10, 10, -5, 5]}

`:.f'(0)=0`, i.e., `f'(0)` is neither `>0` nor `<0`

Hence, `f` is neither `uarr` no `darr`. In fact, it is max. at 0

This can also be viewed from the graph : For `x<0, f` is `uarr` and `for x>0, f` is #darr,