Consider the function f(x)= x+3x^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.

Enter the equations for the asymptotes. If there is no horizontal or vertical asymptote, enter NA in the associated response area.

horizontal asymptote:

vertical asymptote:

(c) Give the intervals of increase and decrease of f(x).

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

If the function is never increasing or decreasing, enter NA in the associated response area.

increasing:

decreasing:

(d) Give the local maximum and minimum values of f(x)

Enter your answers in increasing order of the x-value. If there areless than two local extrema, enter NA in the remaining response areas and the corresponding drop-down menu.

Include a multiplication sign between symbols. For example, a

f( )=

f( )=

(e) Give the intervals of concavity of f(x)

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

If the function is never concave upward or concave downward, enter NA in the associated response area.

concave upward:

concave downward:

(f) Give the inflection points of f(x)

Enter your answers in increasing order of the x-coordinate. If there are less than two points of inflection, enter NA in the remaining response areas.

Include a multiplication sign between symbols.

( , )

( , )