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Suppose f is a function with f(1) = f′(1) = ··· = f^(9) (1) = 0,...

Suppose f is a function with f(1) = f′(1) = ··· = f^(9) (1) = 0, f^(10) (1) = −2, and f^(11) (1) = 3. Write the 11-th Taylor polynomial of f at a = 1, and determine if f has a local maximum or a local minimum or neither at 1.

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