Find The Third Degree Taylor Polynomial For F(X)=X^1/3, Centered At X=1

Answer 1

f(x) = x^1/3

f'(x) = (1/3)x^-2/3

f"(x) = (-2/9)x^-5/3

f'''(x) = (10/27)x^-8/3

Taylor Polynomial: f(1) + f'(1)(x - 1) + [f"(1)/2!](x - 1)² + [f'''(1)/3!](x - 1)³

= 1 + (1/3)(x - 1) - (1/9)(x - 1)² + (5/81)(x - 1)³

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