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Sh1ka9on
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Homework Statement
Continuous function f: R → R, f(x) = 1 - e(x)sin(x)
Continuous function g: R → R, g(x) = 1 + e(x)cos(x)
Homework Equations
Using Rolle's Theorem, prove that between any two roots of f, there exists at least one root of g.
The Attempt at a Solution
I think I'm meant to find an interval (a, b) where g(a)>0 and g(b)<0 then using the Intermediate Value Theorem prove the root. Except I don't know how to go about finding a or b or how Rolle's Theorem comes into play.
Help appreciated.