How to solve this taylor series problem?

Question

obtain the second order taylor polynomial of the function

f(x)=sqrt(x) around x0=64

from the polynomial obtained, estimate the value of sqrt(63) correct to 4 decimal places.

Answer 1

f(x+h)=f(x)+h*f'(x)+((h^2)/2)f''(x) where f(x)=sqrt(x)

f'(x)=1/[2sqrt(x)] and f''(x)=[-1/4(x^(3/2))]

let x=64 and h=-1

then sqrt(63)=8+(-1)(1/16)+(1/2)[-1/4*512]

   =8-(1/16)-(1/1024)

   =8-0.625-0.0009765625

   =7.3740234375