Question

Consider the function f(x)=x−15x^1/3.

For the following questions, write inf for ∞, -inf for −∞, U for the union symbol, None if no answer exists, and separate by a comma if more than one answer exist.

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 =11.18035 and a local minimum at x = 11.180344.

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 function 3 9 10 3
x − x + , find the value of x for which the curve is i) rising ii) f