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I understand that the taylor expansion for a multidimensional function can be written as

[itex]f(\overline{X}[/itex] + [itex]\overline{P}[/itex]) = [itex]f(\overline{X}) + \nabla f(\overline{X}+t\overline{P})(\overline{P})[/itex]

where t is on (0,1).

Although I havent seen that form before, it makes sense.

But I don't understand the integral in the following the Taylor expansion,

[itex]\nabla f(\overline{X}[/itex] + [itex]\overline{P}[/itex]) = [itex]\nabla f(\overline{X}) + \int^{1}_{0} \nabla^{2} f(\overline{X}+t\overline{P})(\overline{P})dt[/itex]

Could someone help me understand the derivation?

Thank you,

Will

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# Taylor expansion, of gradient of a function, in multiple dimensions

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