09. Optimization using derivatives, Obtaining Maximum Area Pens
A farmer has 750 feet of material to build a fence. He wants to enclose a rectangular area and then divide it into four corrals of equal width, with fences parallel to one side of the rectangle. What is the largest possible total area of the four corrals?
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00:00 Introduction and problem statement
00:22 Site diagram and variable assignment
01:06 Modeling the constraint equation (fence length)
02:05 Modeling the function to be maximized (total area)
02:45 Solving for variables and substitution
03:22 Calculating the derivative and critical points
04:33 Verifying the maximum (second criterion) Derivative)
06:05 Calculating Dimensions and Maximum Area
07:11 Viewer Practice Exercise
08:07 Channel Acknowledgments and Memberships
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📗 Calculus with Analytic Geometry, Swokowski
📘 Calculus, Lang
📕 Calculus, Kuratowski
📙 Calculus, Frank Ayres (Schaum's Outline)
📗 Differential and Integral Calculus, Piskunov (MIR)
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