Assume g:(a,b)->R is differentiable at some point c belong to (a,b). If g'(c)not= 0 show that there exists a delta neighborhood V_delta (c) subset or equal to (a,b) for which g(x) not= g(c) for all x belong to V_delta (c).© BrainMass Inc. brainmass.com December 24, 2021, 5:07 pm ad1c9bdddf
Since g'(c) is not 0, without loss of generality, we assume g'(c)>0. We know g'(c) is the limit of (g(x)-g(c))/(x-c) as x->c. When ...
A neighborhood is investigated.