Maximum Area of a Rectangle with Perimeter 20 (Optimization with Derivatives)
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YouTubeMathGPT
Maximum Area of a Rectangle with Perimeter 20 (Optimization with Derivatives)
In this video, we find the maximum possible area of a rectangle with perimeter 20 m. Given: length = x meters, perimeter = 20 Perimeter formula: 2L + 2W = 20 Step 1: Solve for width in terms of x 2x + 2W = 20 x + W = 10 W = 10 - x Step 2: Write area as a function of x A = L * W A(x) = x(10 - x) A(x) = 10x - x^2 Step 3: Differentiate to find the ...
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