Here goes the first one:
prove that for a function f such that its derivative is continuous on [a,b] and derivable on ]a,b[, there exists c E [a,b] st
f(b) = f(a) + (b-a)f'(a) + {1/2}*(b-a)*(b-a)*f''(c)
Not that I don't know the solution, only if someone had a more intelligent solution.
Thanks in advance
aditya


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