1. The problem statement, all variables and given/known data If f is differentiable in an interval I and f' >0 throughout I, except possibly at a single point where f' >=0 then f is stictly incresing on I 2. Relevant equations 3. The attempt at a solution Ok what I have is I let f'(x) >0. I let a and b two points in the interval with a<b. then for some x in (a,b) with F'x= (f(b)-f(a))/b-a but f'(x)>0 for all x in (a,b) so (f(b)-f(a))/(b-a) >0 since b-a>0 it follows that f(b)>f(a) What you can see I have proved that it is incresing in the interval but im not sure what to do when f'=0 any help would be much appreciated as I have been told that it is not fully correct.