Question

How do I use Rolles Theorem to show that f(x)= x^(3)+6x-1 has one zero and it has to be between 0 &1?

Answer 1

ok look
(1) There is at least one real root (via Intermediate Value Theorem).
(2) There is no more than one real root (via Rolle's Theorem). We prove this by contradiction: We assume there are (at least) 2 real roots and deduce a contradiction.

Answer 2

Hope I help! :)

Answer 3

Oh! Ok, so first I need to set up Rolles Theorem and prove that there's only one zero? Is the root and zero the same thing?

Answer 4

I just figured it out! Thanks for your help!