(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let a>b be Real numbers and

f, g: [a,b] --> R be continuous and differentiable on (a,b)

Show g is injective on [a,b] if g'(x) != 0 for all x in (a,b)

2. Relevant equations

Rolle's theorem: Continuity and differentiability (in the conditions above) imply that

f(a) = f(b) and there exists c in (a,b) such that f'(c) = 0

3. The attempt at a solution

Well first I don't know exactly what injective means (what is "distinctness"). What I do understand is Rolle's theorem: that there is a turning point or point of zero gradient between any two points that have the same y-value (if that's right). So in this question there is no turning point or zero gradient in the interval [a,b] - but I don't know what the function is restricted to look like. I'm thinking it could be a horizontal straight line, a parabola, or a squiggly thing that starts and ends between two horizontal points. I'm really quite clueless how to prove something forallsituations

If you could just give me a starting point or outline,

Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Mean Value theorem

**Physics Forums | Science Articles, Homework Help, Discussion**