Let f be a function having derivatives of all orders for all real numbers. Selected values of f and its first four derivatives are shown in the table above.

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Let f be a function having derivatives of all orders for all real numbers. Selected values of f and its first four derivatives are shown in the table above.

(a) Write the second-degree Taylor polynomial for f about x = 0 and use it to approximate f(0.2).

(b) Let g be a function such that g(x) =f(x³). Write the fifth-degree Taylor polynomial for g', the derivative of g, about x = 0.

(c) Write the third-degree Taylor polynomial for f about x = 1.

(d) It is known that |f⁽⁴⁾ (x) | ≤ 300 for 0 ≤ x ≤1.125. The third-degree Taylor polynomial for f about x = 1, found in part (c), is used to approximate f(1.1). Use the Lagrange errór bound along with the

information about f⁽⁴⁾ (x) to find an upper bound on the error of the approximation.

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Let f be a function having derivatives of all orders for all real numbers. Selected values of f and its first four derivatives are shown in the table above.

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Let f be a function having derivatives of all orders for all real numbers. Selected values of f and its first four derivatives are shown in the table above.

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Let f be a function having derivatives of all orders for all real numbers. Selected values of f and its first four derivatives are shown in the table above.