Answer
The linearization of $ f(x)$ at $ x=a $ is also the quadratic approximation of $ f(x)$ at $ x=a $ .
Work Step by Step
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 $.
