Dear students, study today lecture carefully, but please forget the last four minutes (which have been already erased from both the pdf and the video), the ones concerning the implication
f:I-->R, I interval, f continuous on D, f differentiable on int(D)
f'(x) >0 or =0 ==> f increasing.
It is true, but what I said in those final 4 minutes was not enough to prove it