Let's f be a real function on R .Prove if f be differentiable in t with derivative A then :For every e > 0 there be a d >0 such that for every open interval (x1,x2) containing t whose length |x2-x1| is smaller than d ,| (f(x2)- f(x1))/(x2-x1) - A | < eIs its inverse true? Could you provide a contradictory example ? What conditions if f had that would be true?This is useful to better insight to definition of derivatives of measures in topology.