4. Applications of Derivatives

If $f\(\left\)(x\(\right\))=x^3-8x+6$, find the differential $dy$ when x = 2 and $dx = 0.2$.

If $f\left(x\right)=\sqrt{x+2}$, find the differential $dy$ when $x=2$ and $dx=0.01$.

Use a linear approximation (or differentials) to estimate the value of $e^{0.01}$. Which of the following is the best estimate?

Use a linear approximation (or differentials) to estimate the value of ${1.999}^3$.