Problem 1: Determine where the function \( g(x)=x^{3}-4 x^{2}\) has any maximums or minimums. Show the analysis that leads to your conclusion. (5 points) Problem 2: You have \(\$ 8000\) to spend on fencing for a rectangular field. The opposite sides will use special fencing which costs \(\$ 4\) per foot, while the other two sides will use standard fencing costing \(\$ 3\) per foot. What are the dimensions of the largest field you can enclose given the price of the fencing and the money you have to spend? (5 points) Include the following as part of your solution - Draw the field labeling the sides with the variables you choose for the unknowns - Write an equation that represents the cost of the fencing - Write an equation for the area of the field - Combine your two equations and apply calculus to determine the dimensions of the largest field. Problem 3: A certain airline requires that rectangular packages carried on an airplane by passengers be such that the sum of the three dimensions is at most 120 centimeters. Find the dimensions of the square-ended rectangular package of greatest volume that meets this requirement. Include the following as part of your solution - Draw a square-ended rectangular package and label all the sides with the variables you choose for the dimensions. - Write an equation that represents the volume of the package - Write an equation that describes the airline's restrictions. - Combine your two equations and apply calculus to determine the dimensions of the package with greatest volume.