## University Calculus: Early Transcendentals (3rd Edition)

The linearization of $f(x)$ at $x=a$ is also the quadratic approximation of $f(x)$ at $x=a$ .
The linearization of $f(x)$ at $x=a$ is as follows: $L(x) =f(x)=f(a)+(x-a) +f’(a)$ The quadratic approximation of $f(x)$ at $x=a$ is as follows: $Q(x) =f(x)=f(a)+(x-a) +f’(a)+\dfrac{(x-a)^2}{2!}f’’(a)$ Since, $f’’(a)=0$, so $L(x)=Q(x)$ Hence, the linearization of $f(x)$ at $x=a$ is also the quadratic approximation of $f(x)$ at $x=a$.