Download Riemann's example of an integral that is not differentiable

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If lim f ' x  and lim f' x exist,
xc
xc
then they must be equal and they
must equal f ' c.
Mean Value Theorem:
f  x  f c
f ' c  lim
 lim f ' k, x  k  c
x c
x c
x c
f x  f c
f ' c  lim
 lim f ' k, c  k  x
x c
xc
x c
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