for smooth progress toward readiness for further study/careers in science, technology, engineering, and mathematics (STEM) fields. These fluencies are highlighted to stress the need to provide sufficient supports and opportunities for practice to help students gain fluency. Fluency is not meant to come at the expense of conceptual understanding. Rather, it should be an outcome resulting from a progression of learning and thoughtful practice. It is important to provide the conceptual building blocks that develop understanding along with skill toward developing fluency. References: TN State Standards Content Instructional Support & Resources Chapter 3: Applications of Differentiation (Allow approximately 3 weeks for instruction, review, and assessment) Chapter 3 Vocabulary (3-6, 3-7 & Computing and Applying Derivatives 3.6: A Summary of Curve Sketching Domain: Enduring Understandings: Cluster: Apply differentiation techniques The derivative has both theoretical and real life applications. asymptotes, critical numbers, points of Use first and second derivatives to analyze a Additional Resource(s) The derivative provides useful information inflection, test intervals, primary equation, function Larson Calculus Videos Section 3.6 – the behavior of functions and the secondary equation, differential of x, shapes of graphs. differential of y, propagated error, differential s 7. Relate the increasing and decreasing Understanding the rate of change of a form behavior of f to the sign of f’ both analytically function allows you to predict future and graphically. behavior. Writing in Math/Discussion 8. Use the derivative to find extrema (local Essential Questions: Suppose f” (t) < 0 for all t in the interval (2, 8). and global). What does the derivative tell us? Explain why f (3) > f (5). 9. Analytically locate the intervals on which a How can the derivative be used to solve function is increasing, decreasing, or neither. optimization problems? 10. Relate the concavity of f to the sign of f” How do rates of change relate in real-life both analytically and graphically. settings? 11. Use the second derivative to find points of Objectives: inflection as points where concavity changes. Students will:
for smooth progress toward readiness for further study/careers in science, technology, engineering, and mathematics (STEM) fields. These fluencies are highlighted to stress the need to provide sufficient supports and opportunities for practice to help students gain fluency. Fluency is not meant to come at the expense of conceptual understanding. Rather, it should be an outcome resulting from a progression of learning and thoughtful practice. It is important to provide the conceptual building blocks that develop understanding along with skill toward developing fluency. References: TN State Standards Content Instructional Support & Resources Chapter 3: Applications of Differentiation (Allow approximately 3 weeks for instruction, review, and assessment) Domain: Computing and Applying Derivatives Cluster: Apply differentiation techniques Use first and second derivatives to analyze a function 7. Relate the increasing and decreasing behavior of f to the sign of f’ both analytically and graphically. 8. Use the derivative to find extrema (local and global). 9. Analytically locate the intervals on which a function is increasing, decreasing, or neither. 10. Relate the concavity of f to the sign of f” both analytically and graphically. 11. Use the second derivative to find points of inflection as points where concavity changes. Enduring Understandings: The derivative has both theoretical and real life applications. The derivative provides useful information the behavior of functions and the shapes of graphs. Understanding the rate of change of a function allows you to predict future behavior. Essential Questions: What does the derivative tell us? How can the derivative be used to solve optimization problems? How do rates of change relate in real-life settings? Objectives: Students will: 3.6: A Summary of Curve Sketching Additional Resource(s) Larson Calculus Videos – Section 3.6 s Chapter 3 Vocabulary (3-6, 3-7 & asymptotes, critical numbers, points of inflection, test intervals, primary equation, secondary equation, differential of x, differential of y, propagated error, differential form Writing in Math/Discussion Suppose f” (t) < 0 for all t in the interval (2, 8). Explain why f (3) > f (5).
Calculus%20Q3%20%2016-17%20Rev%2011-28-16%20(1).docx