# 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]}