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

Sep 26, 2015

$20 + 8 \left(x - 3\right) + {\left(x - 3\right)}^{2}$

#### Explanation:

$f \left(x\right) = {x}^{2} + 2 x + 5$, f(3)=20

$f ' \left(x\right) = 2 x + 2$, f'(3)=8

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

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

Hence Taylor series expansion would be $20 + 8 \left(x - 3\right) + {\left(x - 3\right)}^{2}$