Question

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

Answer 1

You have to find the derivative and check its sign at `x=0`
It's increasing.

Explanation:

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

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

`f'(x)=3(x+3)^2-8x-2`

At `x=0`

`f'(0)=3(0+3)^2-8*0-2`

`f'(0)=27>0`

Since `f'(0)>0` the function is increasing.