Applications of Derivatives (Part II)
In this unit, scholars will be introduced to some of the most famous applications of derivatives—related rates and optimization. These are some of the real-life applications of the concepts they have been learning about in regards to derivatives. In this unit, scholars will first learn the algebra and concepts behind implicit derivation to prepare them for the process of solving related rates. Next, they will apply their knowledge of derivatives to real-life applications with optimization problems, and finally apply all concepts of the unit together with the challenging applications of related rates. Throughout the unit, emphasis will be given to keeping work neat and to making sure that students understand the concepts they are executing and do not just memorize the steps or an algorithm to solve.
Unit Essential Question:
"What are the real-life applications of derivatives?"
During the calculator portion of the AP Calculus AB examination, it will be assumed that scholars can easily find certain values of a function by using a calculator. This unit is meant to serve both as a refresher of previous calculator skills and to also show scholars how they can use their calculator to quickly find the values of certain derivatives at given x-values. These techniques are meant to build upon the conceptual and algebraic understanding that students have about derivatives. Moving forward, scholars may only use these techniques on calculator-allowed portion of practice/exams and can never use these techniques as their final justification for work. Rather, these skills should be used to confirm what scholars already know!
Unit Resources: Math Bits: http://mathbits.com/MathBits/TISection/Openpage.htm
National Curve Bank: http://curvebank.calstatela.edu/gcal/gcal.htm