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my problem is about of a theorem mathematic,as I prove the following theorem?

F(x)=F(a) + [itex]\sum^{n}_{i=1}[/itex](x[itex]^{i}[/itex]-a[itex]^{i}[/itex])H[itex]_{i}[/itex](x)

good first start with the fundamental theorem of calculus: (for proof):

F(x) - F(a) = [itex]\int^{x}_{a}[/itex]F'(s)ds sustitution: s=t(x - a) + a [itex]\Rightarrow[/itex] [a,x] to [0,1] then:

ds=dt(x - a) later:

f(x) - F(a)= (x - a)[itex]\int^{1}_{0}[/itex]F'(t(x - a) +a)dt

okk my problem is how to get to the sum [itex]\sum[/itex]???

is physic relativistic forum, because of this theorem I can get to the change of coordinates in the Einstein equations and find bases for the manifolds of space-time. thanks!!!

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# Theorem mathematic for relativity

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