Mathematical Methods in Business Assignment Example | Topics and Well Written Essays - 1000 words

Mathematical Methods in Business - Assignment Example The function below approximates the weekly box office receipts for a popular movie, where x = the number of weeks the movie has been playing.  The function below approximates the weekly box office receipts for a popular movie, where x = the number of weeks the movie has been playing.  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                   -15                   -10                  -5                     0                     5                   10                   15                   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 false11. T F When x = 0, the first derivative is positive12. T F When x = 5 the second derivative is positive13. T F When x = 15 the second derivative is positive14. T F the basic shape of this curve is more like an M than a W15. T F For any value of x larger than 15, the first derivative will always be negative