- #1

HHenderson90

- 9

- 0

## Homework Statement

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.)

f(x) = cos 5x, [π/20, 7π/20]

## Homework Equations

Rolles Theorem states:

Let

*f*be a function that satisfies the following three hypotheses:

1. f is continuous on the closed interval [a,b]

2. f is differentiable on the open interval (a,b)

3. f(a)=f(b)

Then there is a number c in (a,b) such that f'(c)=0

## The Attempt at a Solution

1. F is continuous on the closed interval because there is no where on the interval that f(x) is undefined.

2. f is differentiable on the open interval because it is continuous on the closed interval

3. This is where I get confused, these are not a part of the unit circle, do I just plug them into the calculator to determine that f(a)=f(b)?

Then, to find C I must first find the derivative-

f(x)=cos5x

f'(x)=-5sin5x

then I set this equal to 0 to find c

0=-5sin5x

so f'(x)= 0 when x is 0, when the sin5x=0. I don't even know how to go about finding this with numbers that are not on the unit circle.