Problem $3$: $(3$ points$)$ The graph $of{f}^{\text{'}}(x)is$ given below with domain $(-,).$

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

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

$(c)$ Find the $x-$coordinate$(s)$ where $f(x)$ achieves a local maximum.

$(d)$ Find the $x-$coordinate$(s)$ where $f(x)$ achieves a local minimum.

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

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