Let $f(x)=x^3-9x^2$

Calculate the derivative

$f^{\text{'}}(x)=$

$$

Calculate the second derivative

$f^{\text{'}\text{'}}(x)=$

$$

Note intervals are entered in the format $(-00,5)(7,)($these are two infinite intervals$).$

On what interval$($s$)$ is $f$ increasing?

Increasing: $$

On what interval$($s$)$ is $f$ decreasing?

Decreasing: $$

On what interval$($s$)$ is $f$ concave downward?

Concave Down: $$

On what interval$($s$)$ is $f$ 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: $$