Calculus
posted by David on .
a) prove that the function x^3 + 9x^2 +33x assumes the value 8 at least once
b)using the mean value theorom or rolle's theorom  no other methods will be accepted  prove carefully that x^3 + 9x^2 + 33x takes on the value 8 at most once

a.
determine the domain and range of the function and conclude.
b.
Prove by contradiction:
assume that there are two or more values of x for which f(x1)=8 and f(x2)=8, where x1<x2.
Consider the interval [x1,x2], and apply Rolle's theorem or the mean value theorem to see if it is possible to find such x1, x2.