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Optimization Problem - Inscribed Rectangle with Max Area | JK Math
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In this video we look at how to solve the following optimization problem: A rectangle is bounded by the x-axis and the semicircle y=√(25-x²). What length and width should the rectangle have so that its area is a maximum?
Video Chapters:
0:00 Step 1: Problem Reading
0:50 Step 2: Setting up Primary Equation for Area
3:08 Step 3: Using the Constraint
5:36 Step 4: Domain (What values make sense?)
9:12 Step 5: Taking the Derivative & Solving for x
19:14 Step 6: Using x to find y & the Length & Width
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