'campground owner has 2400 m of fencing: He wants to enclose a rectangular field bordering a river; with no fencing along the river: (See the sketch:) Let X represent the width of the field. River (a) Write an expression for the length of the field as a function of X (b) Find the area of the field (area = length x width) as a function of X. (c) Find the value of x leading to the maximum area (d) Find the maximum area_ (a) %(x) ='
Added by Christopher S.
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Step 1: The length of the field as a function of X is given by \( y = 2400 - 2x \). Show more…
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Carson M.
A campground owner has 1200 m of fencing. He wants to enclose a rectangular field bordering a river, with no fencing along the river. (See the sketch.) Let x represent the width of the field. (a) Write an expression for the length of the field as a function of x. (b) Find the area of the field (area = length x width) as a function of x. (c) Find the value of x leading to the maximum area. (d) Find the maximum area. (a) l(x) = (b) A(x) = (c) First write the expression for the derivative used to find the x value that maximizes area. dA/dx = The x-value leading to the maximum area is (d) The maximum area of the rectangular plot is
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A rancher has 200 feet of fencing to enclose two adjacent rectangular corrals (see figure). (a) Write the area $ A $ of the corrals as a function of $ x $. (b) Create a table showing possible values of $ x $ and the corresponding areas of the corral. Use the table to estimate the dimensions that will produce the maximum enclosed area (c) Use a graphing utility to graph the area function. Use the graph to approximate the dimensions that will produce the maximum enclosed area. (d) Write the area function in standard form to find analytically the dimensions that will produce the maximum area. (e) Compare your results from parts (b), (c), and (d).
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