# Taylor series

Hi ,
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.

Thank you

Related Introductory Physics Homework Help News on Phys.org
HallsofIvy
Homework Helper
Yes, you should use the remainder theorem. You would find the remainder after n terms for the Taylor's series in terms of (x- 4.5)n. Of course, here x- 4.5= 5.8- 4.5= 1.3. For what n is the remainder less than 0.0000001?

What is the maximum possible value of |11x- 28- x2| for 4< x< 6?

ok,
thank I think i get it.

HallsofIvy said:
Yes, you should use the remainder theorem. You would find the remainder after n terms for the Taylor's series in terms of (x- 4.5)n. Of course, here x- 4.5= 5.8- 4.5= 1.3. For what n is the remainder less than 0.0000001?

What is the maximum possible value of |11x- 28- x2| for 4< x< 6?