First Derivative Test

$$f'\left(x\right)=\ 2x\left(x^2-3\right)$$

Over what intervals is f(x) decreasing?

Which of the following could be the graph of f ' , the derivative of f ?

If  $$f'\left(a\right)=0$$  and  $$f'\left(x\right)$$  changes from negative to positive at  $$x=a$$  , then  $$f\left(x\right)$$  has 

The function  $$f\left(x\right)=-x^3+3x^2-5$$  has a relative minimum at:

Identify the critical points of the following function: $$g(x)=\frac{x^3}{x+1}$$

If the first derivative of a function changes from positive to negative at a certain point, then that point is a known as a relative maximum.

Given a function $$f(x),\ if\ f'(x)<0$$ over a certain interval, then $$f(x)$$ is ____________ over that interval.