5. 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 $f\left(16.01\right)$.