IMathAS-libretexts

Let $\displaystyle {f{{\left({x}\right)}}}={x}^{{3}}-{3}{x}^{{2}}+{3}{x}+{3}$ .

Calculate the derivative
$\displaystyle {f}'{\left({x}\right)}=$

Calculate the second derivative
$\displaystyle {f}{''}{\left({x}\right)}=$

Note intervals are entered in the format (-00,5)U(7,oo) (these are two infinite intervals). Enter "DNE" if the interval is empty.

On what interval(s) is $\displaystyle {f}$ increasing?
Increasing:

On what interval(s) is $\displaystyle {f}$ decreasing?
Decreasing:

On what interval(s) is $\displaystyle {f}$ concave downward?
Concave Down:

On what interval(s) is $\displaystyle {f}$ concave upward?
Concave Up:

What is the limit as x approaches infinity?
Limit is:

What is the limit as x approaches negative infinity?
Limit is:

Sketch the graph and submit with your work.