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The function has derivatives of all orders within its radius of convergence of . Its Maclaurin series is .

  1. What are the coefficients of the first-degree and second-degree terms of ? Use those coefficients to determine if has a local maximum, local minimum or neither at . Justify your answer.

  2. Expand the Maclaurin series for out to four terms to create a fifth-degree Taylor polynomial centered at , . Then write the antiderivative of .