Given $f(x)=x^3+3x^2-105x+13$

When asked to find an interval, use interval notation and enter an open interval.

Use a comma separated list to enter multiple answers.

If an answer does not exist, enter DNE.

Part a$)$ Find the interval$($s$)$ where $f$ is increasing.

$f$ is increasing on $$

Part b$)$ Find the interval$($s$)$ where $f$ is decreasing.

$f$ is decreasing on $$

Part c$)$ Find the local minimum and the local maximum values.

Local minimum value $=$

Local maximum value $=$

Part d$)$ Find the inflection point.

$$

$(x,y)=$

Part e$)$ Find the interval$($s$)$ where $f$ is concave up$.$

$f$ is concave up on $$

Part f $)$ Find the interval$($s$)$ where $f$ is concave down.

$f$ is concave down on $$