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I have some difficulties to solve this problem. It is from my numerical methods class but the problem is about taylor series:

It is known that for 4 < x < 6, the absolute value of the m-th derivative of a certain function f(x) is bounded by m times the absolute value of the quadratic 11x-28-x2. That is, |f(x)(m)| < m|11x - 28 - x2| for m > 0. How many terms would be required in the Taylor series for f about x = 4.5 to evaluate f(5.8) accurate to 7 decimals?

Please, I need some sugestions. I am not sure if i need to use the remainder formula to find it.

Please somebody help me!

Thank you

Brad

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# Taylor series

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