Question

Help with intermiadiate value Theorem please

Answer 1

The Intermediate Value Theorem guarantees the existence of at least one real zero of the polynomial function 1/3x^3 - 3 on all the following intervals except:

Answer 2

@kirbykirby

Answer 3

The IVT essentially says that if a function \(f\) is continuous over an interval \([a,b]\), then at least one zero is certain to exist provided that \(f(a)<0<f(b)\) or \(f(b)<0<f(a)\).

This means you'll need to evaluate the given function at the listed intervals' endpoints. If you find that one endpoint gives a function value that is negative, while the other is positive (or vice versa), then the IVT can be used to state that a zero exists in the interval.