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Compose a 1000 words assignment on mathematical methods in business. Needs to be plagiarism free! The function below approximates the weekly box office receipts for a popular movie, where x = the number of weeks the movie has been playing.&nbsp.The function below approximates the weekly box office receipts for a popular movie, where x = the number of weeks the movie has been playing.&nbsp.What is the rate of change of weekly receipts per theater after 10 weeks?The selling price of a product is \$400, and the manufacturer is able to sell every unit it makes. The cost of producing x units is given by this formula.A company has developed a function that describes its profit over time. The x variable measures time. If the first derivative of the function is negative at a value of x, it means that the company is not making a profit at that point in time.A function has the characteristics listed in the bullets below. Use the characteristics to construct a rough sketch of the function using this x axis:_________________________________________________________________________________-20 &nbsp. &nbsp. &nbsp. &nbsp. &nbsp. &nbsp. -15 &nbsp. &nbsp. &nbsp. &nbsp. &nbsp. &nbsp. -10 &nbsp. &nbsp. &nbsp. &nbsp. &nbsp. &nbsp.-5 &nbsp. &nbsp. &nbsp. &nbsp. &nbsp. &nbsp. &nbsp.0 &nbsp. &nbsp. &nbsp. &nbsp. &nbsp. &nbsp. &nbsp.5 &nbsp. &nbsp. &nbsp. &nbsp. &nbsp. &nbsp. 10 &nbsp. &nbsp. &nbsp. &nbsp. &nbsp. &nbsp. 15 &nbsp. &nbsp. &nbsp. &nbsp. &nbsp. &nbsp. 20• The function has three critical points• When x = -20, the first derivative is positive• When x = -10, the first derivative is zero and the second derivative is negative• When x = 5, the first derivative is zero• When x = 15, the first derivative is zero indicates whether each of these statements is true or false