Question

How do you determine the intervals for which the function is increasing or decreasing given `f(x)=-x^3-2x+1`?

Answer 1

`f(x)` is always decreasing function and in interval notation it is decreasing for `(-oo,oo)`

Explanation:

For the function `f(x)=-x^3-2x+1`, as `x->oo`, `f(x)->-oo` and as `x->-oo`, `f(x)->oo`

As `(df)/(dx)=f'(x)=-3x^2-2` and as `x^2` is always positive,

`f'(x)` is always negative and hence

`f(x)` is always decreasing function and in interval notation it is decreasing for `(-oo,oo)`

graph{-x^3-2x+1 [-40, 40, -20, 20]}