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- Taylor series expansion or polynomial regression which is the correct term here for finding an analytical estimate for an unknown function?

Hello,

I have a question regarding the Taylor expansion of an unknown function and I would be tanksful to have your comments on that.

Suppose we want to find an analytical estimate for an unknown function. The available information for this function is; its exact value at x0 (f0) and first derivative at x0 (f0'), and its exact value at x=x1 (f1) which is far from x0. This means that we only need to find the second derivative through solving f1 = f0 + f0'*(x1-x0) + (f"0/2)*(x1-x0)^2 to form the truncated Taylor series for f.

My question is that whether the obtained quadratic function is the result of Taylor series expansion or polynomial regression?

I have a question regarding the Taylor expansion of an unknown function and I would be tanksful to have your comments on that.

Suppose we want to find an analytical estimate for an unknown function. The available information for this function is; its exact value at x0 (f0) and first derivative at x0 (f0'), and its exact value at x=x1 (f1) which is far from x0. This means that we only need to find the second derivative through solving f1 = f0 + f0'*(x1-x0) + (f"0/2)*(x1-x0)^2 to form the truncated Taylor series for f.

My question is that whether the obtained quadratic function is the result of Taylor series expansion or polynomial regression?

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