Consider the function f(x)=x-9x^(1/3)

Question

a.) The domain of this function: (-INF,INF)

b.) The x-intercept(s):_____ and the y intercept(s): 0

c.) The critical number(s):

d.) f(x) is increasing on the interval(s) _____ and decreasing on ______

e.) f(x) has a local maximum at x=-3^(3/2) and a local minimum at x=3^(3/2)

f.) f(x) is concave up on the interval(s) _____ and concave down on ______

g.) f(x) has one point of inflection at x= 0

h.) The horizontal asymptote is y=None and the vertical asymptote is x=None

Answer 1

The easiest way to answer this question is to graph the function and if you don't have a graphing calculator, sketch it

f = 0 at 0, 27 and -27

it has a minimum at x=sqrt(27) a max at x = -sqrt(27)

and a point of inflection at x = 0

and is unbounded positively when x is large and unbounded negatively when x goes to negative infinity