Select either the minimum or maximum function. Identify a task - personal or professional - that could be modeled mathematically through your chosen function. Explain how the chosen function can be us

Select either the minimum or maximum function. Identify a task - personal or professional - that could be modeled mathematically through your chosen function. Explain how the chosen function can be used in making good decisions. Examples of tasks might be:

Make the largest garden possible using a given amount of fencing.

Configure an airplane to create the least amount of drag for an airplane in flight. 

Be creative!

This question is referring to minima and maxima of derivatives, and is encouraged to detail at least one inflection. 

we are being asked to write three paragraphs detailing the information.

the question i would like to write about is ,   The solar-energy power P (in W) produced by a certain solar system does not rise and fall uniformly during a cloudless day because of the system’s location. An analysis of records shows that P = -0.4512t5 - 45t4 + 350t3 - 1000t22, where t is the time (in h) during which power is produced. Show that, during the solar-power production, the production flattens (inflection) in the middle and then peaks before shutting down. (Hint: The solutions are integral.) .... However, I am open to any creative suggestions. 

Thank you.