Chapter 4.3, Problem 142E

For the following exercises, consider the production of gold during the California gold rush (1848-1888). The production of gold can be modeled by $G\left(t\right)=\frac{\left(25t\right)}{\left(t^2+16\right)}$ , where t is the number of years since the rush began $\left(0\le t\le 40\right)$ and G is ounces of gold produced (in millions). A summary of the data is shown in the following figure.

142. Find when the maximum (local and global) gold production occurred, and the amount of gold produced during that maximum.