- #1

dancergirlie

- 200

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## Homework Statement

Consider a function g : (a, b)-->R. Assume that g is differentiable at some point c in

(a,b) and that g'(c) is not = 0. Show that there is a delta > 0 so that g(x) is unequal to g(c) for all x in V_delta(c)\{c}intersect(a,b)

## Homework Equations

## The Attempt at a Solution

Alright, this is what I tried so far:

Since g is differentiable at c that means that

g'(c)=lim_x-->c (g(x)-g(c)/x-c)

since we are assuming that g'(c) is unequal to 0 that means that

lim_x-->c (g(x)-g(c)/x-c) is unequal to zero and thus g(x)-g(c) is unequal to zero

and therefore g(x) is unequal to g(c).

I don't really know where the delta comes in though, am I supposed to use the definition of a limit to show that there exists an epsilon greater than zero so that for |g'(c)-L|<epsilon?

Any help would be great!