Consider the function $f(x)=x+3x^{\frac{2}{3}}$

$($a$)$ Find the domain of $f(x).$

Note: Use the letter U for union. To enter $,$ type infinity with a lower case i$.$

Domain: $$

$($b$)$ Give the horizontal and vertical asymptotes of $f(x),$ if any.

$($C$)$ give the intervals of increase and decrease of f$($x$)$

$($D$)$ give the local maximum and minimum values of f$($x$)$

Enter answer in increasing order of the value of x

$($e$)$ give the intervals lf concavity of f$($x$)$