Questo teorema afferma che se una funzione e' continua in un intervallo chiuso e limitato e derivabile all'interno dell'intervallo stesso e se inoltre agli estremi dell'intervallo assume lo stesso valore allora esiste almeno un punto dell'intervallo in cui la derivata della funzione vale 0.
as seen from the figure in practice means that if the function starts at a certain level and reaches the same value without spikes and then if 'continues and if the interval and' closed bounded there must be a point where it stopped increasing (or decrease) and back (you can 'also say that the tangent at that point and' horizontal)
Mathematically:
if y = f (x) and 'a continuous function in a closed and bounded interval [a, b ] such that f (a) = f (b) then there exists a point c belonging to [a, b] such that f '(c) = 0
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Using this theorem in both oral and written many checks is that it must
test four hypotheses that the function is continuous
that the function is differentiable
within the range that the range is closed and limited
that the values \u200b\u200bat the extremes of the range are equal
now tries to prove that the theorem does not and 'occurred (ie' do an example where the theorem is not valid) if it lacks the former, or the third or second and third ...
understand that to solve it you have to think and to know exactly what is meant by a continuous function, closed bounded interval by interval and so on.
After trying to just compare these examples with the rather good and some that do not include all possible cases
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