{"id":244756,"date":"2023-11-24T10:17:48","date_gmt":"2023-11-24T15:17:48","guid":{"rendered":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/optimization-models-and-rates-of-change-advanced-placement-calculus-12th-grade"},"modified":"2023-11-24T10:17:48","modified_gmt":"2023-11-24T15:17:48","slug":"optimization-models-and-rates-of-change-advanced-placement-calculus-12th-grade","status":"publish","type":"post","link":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/optimization-models-and-rates-of-change-advanced-placement-calculus-12th-grade","title":{"rendered":"Optimization Models and Rates of Change – Advanced Placement Calculus – 12th Grade"},"content":{"rendered":"

As part of the Advanced Placement Calculus course directed by Jos\u00e9 Luis Zamora, we were introduced to optimization models and rates of change problems parting from the initial concept of derivatives. Within this process, we obtained the necessary knowledge to develop two different problems: one for optimization and one for rates of change. We, Gabriela Orjuela Dorado and Carlos Pe\u00c3\u00b1a, created a virtual poster to present both models. Product of hard work and commitment, the first problem showcasing changes in position, speed\/velocity, and acceleration through simple harmonic motion was addressed using the graphing tool Geogebra. The second problem, showcasing the perfect example of both related ratios and optimization, was addressed by de-constructing a 3D image and designing a live simulation. Together with other conclusions, we formulated equations that defined the behavior of the situations described and predicted possible changes in its variables.
This project poses critical and advanced thinking, given that in order to work with the eText from the Pearson platform a detailed understanding of the natural world of both physics and calculus, was required. The most challenging part of this project’s process was combining all previously acquired knowledge. With perseverance, and more than three failed trials, we were finally able to design the best fitting mathematical models to solve the questions presented to us.
Now, if you want to take a look at the virtual poster containing the different products and processes of this project, we invite you to access the following QR code. Sneak peak: what you can achieve using Geogebra.<\/p>\n

\"\"<\/p>\n

Jose Luis Zamora
High School Mathematics Teacher<\/b><\/p>\n

Gabriela Orjuela Dorado and Carlos Pe\u00c3\u00b1a
Twelfth Grade AP Calculus Students<\/b><\/p>\n

Resumen:<\/b>En el curso de AP C\u00c3\u00a1lculo de Jos\u00e9 Luis Zamora comenzamos el tema de modelos de optimizaci\u00c3\u00b3n y razones relacionadas partiendo de lo que conocemos de derivadas. A partir de este proceso obtuvimos el conocimiento necesario para desarrollar dos problemas diferentes: uno de optimizaci\u00c3\u00b3n y otro de razones relacionadas. Nosotros, Gabriela Orjuela Dorado y Carlos Pe\u00c3\u00b1a, creamos un p\u00c3\u00b3ster virtual para presentar ambos modelos. Producto de compromiso y un arduo trabajo, el primer problema que retrata cambios de posici\u00c3\u00b3n, velocidad y aceleraci\u00c3\u00b3n a trav\u00e9s de un movimiento arm\u00c3\u00b3nico simple, se abord\u00c3\u00b3 utilizando la herramienta gr\u00c3\u00a1fica Geogebra. El segundo problema, que muestra el ejemplo perfecto tanto de razones relacionadas como de optimizaci\u00c3\u00b3n, se abord\u00c3\u00b3 deconstruyendo una imagen 3D a su respectiva representaci\u00c3\u00b3n en 2D y dise\u00c3\u00b1ando una simulaci\u00c3\u00b3n. Junto con otras conclusiones, formulamos ecuaciones que definen el comportamiento de las situaciones descritas y predec\u00c3<\/p>\n","protected":false},"excerpt":{"rendered":"

As part of the Advanced Placement Calculus course directed by Jos\u00e9 Luis Zamora, we were introduced to optimization models and rates of change problems parting from the initial concept of derivatives. Within this process, we obtained the necessary knowledge to develop two different problems: one for optimization and one for rates of change. We, Gabriela […]<\/p>\n","protected":false},"author":1,"featured_media":244757,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":""},"categories":[1],"tags":[61],"_links":{"self":[{"href":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/wp-json\/wp\/v2\/posts\/244756"}],"collection":[{"href":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/wp-json\/wp\/v2\/comments?post=244756"}],"version-history":[{"count":0,"href":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/wp-json\/wp\/v2\/posts\/244756\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/wp-json\/wp\/v2\/media\/244757"}],"wp:attachment":[{"href":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/wp-json\/wp\/v2\/media?parent=244756"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/wp-json\/wp\/v2\/categories?post=244756"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/wp-json\/wp\/v2\/tags?post=244756"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}