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###### Let fbe a functions that has derivatives of all orders for all real numbers_ Assume f (0) = -1,f' (0) = 3,f" (0) = 2 and f" (0) = 4 a) Write the third degree Taylor Polynomials for f (2) about x 0_ b) Use the polynomial from (a) to approximate f (1) _ The fourth derivative of f (c) satisfies the inequality | f(4) (.)| < 3 for all x in the interval [0, 1]. Use the Lagrange error bound to find the size of the error in the approximation of f (1).a) The third degree Taylor polynomi

Let f be a functions that has derivatives of all orders for all real numbers_ Assume f (0) = -1,f' (0) = 3,f" (0) = 2 and f" (0) = 4 a) Write the third degree Taylor Polynomials for f (2) about x 0_ b) Use the polynomial from (a) to approximate f (1) _ The fourth derivative of f (c) satisfies the inequality | f(4) (.)| < 3 for all x in the interval [0, 1]. Use the Lagrange error bound to find the size of the error in the approximation of f (1). a) The third degree Taylor polynomial is b) The approximation of f (1) is The Lagrange Error bound is

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