# How do you verify that the function #f(x)= sin(22pix)# satisfies the three hypotheses of Rolle's Theorem on the given interval [-1/11, 1/11] and then find all numbers c that satisfy the conclusion of Rolle's Theorem?

##### 1 Answer

In this context, "Verify" mean "Prove" or "Show". Think of this as a writing assignment.

"Convince a reader that the function

(Then do some algebra to prove to your grader (1) I know what the conclusion says and (2) I can do algebra to solve an equation.)

Go through the hypotheses in order and tell you reader why they should agree that the hypothesis is true for this function on this interval:

**H1: The function #f(x)= sin(22pix)# is continuous on the closed interval # [-1/11, 1/11]#** , because:

the 'inside' function

**H2: The function #f(x)= sin(22pix)# is differentiable on the open interval # (-1/11, 1/11)#** , because:

**H3: The function has equal values at the endpoints or the interval**

We have now verified that the function

The conclusion of Rolle's Theorem tells us that there is a number

In this case, there is a number

From trigonometry we know that the solutions are:

So

Taking