Use the equation to show  the maximum, minimum, and minimum in the future. 

For each queation please show the steps, explain the approuch behind it, explain the important steps in the computation, and explain the result in the context of the problem.

A small business selling sun-glasses has seen a mostly linear growth in profits over 2020, though there was also a seasonal impact. The data from 2020 was used to create a model for the profit per month P as a function of the number of months since the beginning of 2020

P= f(m) = 1000m - (12000/?) cos((?/6)m)

Use differentiation methods for the following:
1. Use the equation to show that the maximum profit in 2020 occured at the end of July, when m=7.
2. Show that the model predicts there will be a local minimum in profit at the end of November 2021, when    m= 23.
3. Show that the model predicts that the minimum profit in 2021 will occur at the beginning of January, when m= 12.

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  • Please allow at least a few hours. One hour is too short for such questions with multiple parts.

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