Largest area of a rectangle inscribed in a semicircle (KristaKingMath)

► My Applications of Derivatives course: www.kristaking...
Learn how to find the largest area of a rectangle that can be inscribed inside a semicircle, given that the semicircle has radius r. Since this is an optimization problem, draw a picture of the problem and write what you know. Then identify optimization and constraint equations. Solve the constraint equation for one of the variables, and plug the solution into the optimization equation to get the optimization equation in terms of one variable. Then take the derivative of the optimization equation, set it equal to zero, and solve for the variable. Make sure to answer the question you were asked!
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
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