Recent content by michaeldoe

##f''(\xi(x))## comes from Taylor's theorem with the Lagrange form of the remainder. This theorem is actually what is used in the original post to prove/derive the error term for the Midpoint Rule (a numerical method of integration): $$ \frac{h^2(b-a) f''(\xi)}{24} $$ The value ##\xi## depends...

The screenshot I have attached is actually what is being done (the whole proof, if that's what you meant). Also, yesterday I have read more and it seems I have understood the actual difference between two versions of MVTI for weaker (integrability only) and stronger case. When ##f## is not...

I have found the following proof of remainder term for midpoint rule of integration: and I'm trying to understand the part of it where author is applying MVTI to composition of functions ##f''(\xi_i(x))## and move it out of integral sign as ##f''(\xi_i)##. If we solve Taylor's series for this...