## Calculus (3rd Edition)

$$f(x)= =1+2(x-3)+6(x-3)^2+\frac{1}{2}(x-c)^3+..$$
The first four terms of the Taylor series of $f (x)$ centered at $c = 3$ are: $$f(x)=f(c)+f'(c)(x-c)+f''(c)(x-c)^2/2!+f'''(c)(x-c)^3/3!+...\\ =1+2(x-3)+6(x-3)^2+\frac{1}{2}(x-c)^3+..$$