# Rolle's Theorem question?

#### Tompo

##### New member
[h=1][/h]I'm doing a question and I am getting stuck and need help

Question:
Consider the continuous functions f(x) = 1 - e^(x)*sin(x) and g(x) = 1 + e^(x)*cos(x). Using Rolle's Theorem, prove that between any two roots of f there exists at least one root of g.

Hint
Remember that, a root of f is a point x in the domain of f such that f(x) = 0.

Can someone provide a natural language proof of this?

#### MarkFL

$\displaystyle -e^c\cos(c)-e^c\sin(c)=0$
$\displaystyle -e^c\sin(c)=e^c\cos(c)$
$\displaystyle 1-e^c\sin(c)=1+e^c\cos(c)$
$\displaystyle f(c)=g(c)$