Maximize Volume of an Open Top Box (Optimization) | Calculus 1 Exercises

We solve a common type of optimization problem where we are asked to find the dimensions that maximize the volume of an open top box with a square base and a fixed surface area. To do this we begin with a volume equation then use the surface area restriction to rewrite the volume in terms of a single variable, at which point we can use our usual strategy of taking the first derivative, finding critical points, then using the first or second derivative test to classify these critical points. #Calculus1 #apcalculus Calculus 1 Exercises playlist:    • Calculus 1 Exercises   Calculus 1 playlist:    • Calculus 1   ◉Textbooks I Like◉ Graph Theory: https://amzn.to/3JHQtZj Real Analysis: https://amzn.to/3CMdgjI Proofs and Set Theory: https://amzn.to/367VBXP (available for free online) Statistics: https://amzn.to/3tsaEER Abstract Algebra: https://amzn.to/3IjoZaO Discrete Math: https://amzn.to/3qfhoUn Number Theory: https://amzn.to/3JqpOQd ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits:   / wrathofmathlessons   ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Thanks to Petar, dric, Rolf Waefler, Robert Rennie, Barbara Sharrock, Joshua Gray, Karl Kristiansen, Katy, Mohamad Nossier, and Shadow Master for their generous support on Patreon! Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu   My Math Rap channel:    / @mathbars2020