Question

How can you find the taylor expansion of `f(x) = x^2 + 2x + 5` about x=3?

Answer 1

`20+ 8(x-3)+ (x-3)^2`

Explanation:

`f(x)= x^2+2x+5`, f(3)=20

`f'(x)= 2x+2`, f'(3)=8

#f"(x) =2, f"(3)=2

f'''(x) and all other drivatives would be 0

Hence Taylor series expansion would be `20+8(x-3) +(x-3)^2`