Question: A rectangle in the first quadrant has its base on the \(x\) -axis, its left side on the \(y\) -axis and its upper right corner on the graph of \(f(x)=\frac{60}{x+e^{6 x}}\) (see diagram).

1. Showing all work, use calculus techniques to analytically determine the maximum possible area of the rectangle. Give an exact simplified answer. Your solution should include the domain of the function being optimized and an appropriate test of \(\max / \mathrm{min}\) (include the name of the test used).
2. Enter the maximum area below. Round your answer to 2 decimal places if appropriate.

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