Let $f^{}\left(x\right)=h\left(g\left(x\right)\right)$. Calculate $f^{\prime }\left(0\right)$ using the following table:

Determine the derivative of the function $f\left(x\right)=2x^3$ using the definition:

$f^{\prime }\left(x\right)=\underset{h\to 0}{\lim }\frac{f(x+h)-f\left(x\right)}{h}$

Given the function $g\left(x\right)=\frac{18}{x^2}$, find $g^{\prime }\left(x\right)$ using the limit definition of the derivative. Then, calculate the value of $g^{\prime }\left(5\right)$.

The graph of the derivative of $f\left(x\right)=\mid 2x\mid$ is shown. Graph $y=\frac{\mid 2x\mid -0}{x-0}=\frac{\mid 2x\mid }{x}$. What can you conclude after graphing?

The population of rabbits in a fenced reserve from the year $2000$ to $2010$ is represented by the graph provided. Determine the year in which the population's growth rate was at its highest.