Hi, I'm really having a hard time with this homework especially part b through d. I have some major errors in my calculations with only some parts being correct. Can you help me?

Consider the function f (x) = x + 6x 3 (a) Find the domain of f (a). Note: Use the letter U for union. To enter oo, type infinity with a lower case i. Domain: (-infinity, infinity) (b) Give the horizontal and vertical asymptotes of f (x), if any. Enter the equations for the asymptotes. If there is no horizontal or vertical asymptote, enter NA in the associated response area. horizontal asymptote: y = infinity vertical NA asymptote: (c) Give the intervals of increase and decrease of f (a). Note: Use the letter U for union. To enter co, type infinity with a lower case i. If the function is never increasing or decreasing, enter NA in the associated response area. increasing: NAincreasing: NA @ D decreasing: (ell'lnlty 764') u (754' innity: @ D (I!) Give the local maXimum and minimum values of f (:13) Enter your answers in increaSing order of the xevalue, If there are less than two local extrema, enter NA in the remaining response areas and the corresponding dropdown menu, Include a multiplication Sign between symbols For example, a - 1r, f( 434 E D )= 8176 B H isalocalmaximum v f( NA so )= NA m ~A - (3) Give the intervals of concaVIty of f (it). Note Use the letter U for union, To enter on, type innity With a lower case i If the function is never concave upward or concave downward enter NA in the associated response area, concave upward: (rinnityim E 1? concave D innit l downward: (' y, E 3 (fl Give the inflection paints of f [23)