4. Applications of Derivatives

If $f\(\left\)(x\(\right\))=x^3+1$, use the linearization $L\(\left\)(x\(\right\))$ at $a=5$ to approximate $f\(\left\)(5.1\(\right\))$.

If $f\left(x\right)=\sqrt{x}+12$, use the linearization $L\left(x\right)$ at $a=16$ to approximate $f\left(16.01\right)$.

What is the value of the local linearization of the function $f\left(x\right)=x^2$ at $x=2$, evaluated at $x=2.1$?