This cannot happen. f is assumed bounded. Therefore the average of f’ over the interval [a,b] tends to zero as the bounds go to infinity.
The precise, complete mathematical statement and proof of the theorem does involve some subtlety of argument (consider what happens if f = sin(exp(x))) but the theorem is correct.
This cannot happen. f is assumed bounded. Therefore the average of f’ over the interval [a,b] tends to zero as the bounds go to infinity.
The precise, complete mathematical statement and proof of the theorem does involve some subtlety of argument (consider what happens if f = sin(exp(x))) but the theorem is correct.