Let f be a function that has derivatives of all orders for all real numbers. Assume f(1)=3, f'(1)=-2, f"(1)=2, and f'''(1)=4(adsbygoogle = window.adsbygoogle || []).push({});

a. Write the second-degree Taylor polynomial for f about x=1 and use it to approximate f(0.7).

b. Write the third-degree Taylor polynomial for f about x=1 and use it to approximate f(1.2).

c. Write the second-degree Taylor polynomial for f', the derivative of f, and x=1 and use it to approximate f'(1.2).

a. T{2}(x) = f(1) + f'(1)(x-1) + f"(1)(x-1)^2/2!

plug in .7 = 3.51

b. T{3}(x) = f(1) + f'(1)(x-1) + f"(1)(x-1)^2/2! + f"'(1)(x-1)^3/3!

plug in 1.2 = 2.64

c. What do I do for c?

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# Taylor Polynomials

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