How do you verify that the function #f(x)= (sqrt x)- 1/3 x# satisfies the three hypothesis of Rolles's Theorem on the given interval [0,9] and then find all numbers (c) that satisfy the conclusion of Rolle's Theorem?
1 Answer
Explanation:
1)
2)
3)
So Rolle's theorem states that
(Notice that Rolle's theorem doesn't give you the exact number of
So we have to find out that
So we have only one
If you look at the graph you can convince yourself the answer is correct and the meaning of Rolle's theorem
(although, a graph is not a proof)
graph{sqrt(x) -1/3x [-10, 10, -5, 5]}