# Contextual Applications of the Derivative – Unit 4

Unit 4 covers rates of change in motion problems and other contexts, related rate problems, linear approximation, and L’Hospital’s Rule. (CED – 2019 p. 82 – 90). These topics account for about 10 – 15% of questions on the AB exam and 6 – 9% of the BC questions. You may want to consider teaching Unit…

# 2019 CED Unit 4: Contextual Applications of the Derivative

Unit 4 covers rates of change in motion problems and other contexts, related rate problems, linear approximation and L’Hospital’s Rule. (CED – 2019 p. 82 – 90). These topics account for about 10 – 15% of questions on the AB exam and 6 – 9% of the BC questions. Topics 4.1 – 4.6 Topic 4.1 Interpreting…

# Extreme Values and Linear Motion

Two more applications of differentiation are finding extreme values and the analysis of linear motion. Extreme Values The Marble and the Vase Extremes without Calculus A Standard Problem Far Out! Linear Motion – Motion on a Line  Type 2 Problems Motion Problems: Same Thing, Different Context The Ubiquitous Particle Motion Problem  – a PowerPoint Presentation and…

# Linear Motion (Type 2)

“A particle (or car, or bicycle) moves on a number line ….” These questions may give the position equation, the velocity equation or the acceleration equation of something that is moving, along with an initial condition. The questions ask for information about motion of the particle: its direction, when it changes direction, its maximum position…

# Parametric and Vector Equations

AP Type Questions 8 Particle moving on a plane for BC – the parametric/vector question. I have always had the impression that the AP exam assumed that parametric equations and vectors were first studied and developed in a pre-calculus course. In fact many schools do just that. It would be nice if students knew all…

# Motion on a Line

AP Type Questions 4 These questions may give the position equation, the velocity equation or the acceleration equation of something that is moving, along with an initial condition. The questions ask for information about motion of the particle: its direction, when it changes direction, its maximum position in one direction (farthest left or right), its…

# Motion Problems: Same Thing, Different Context

Calculus is about things that are changing. Certainly, things that move are changing, changing their position, velocity and acceleration. Most calculus textbooks deal with thing being dropped or thrown up into the air. This is called as uniformly accelerated motion since  the acceleration is due to gravity and is a constant. While this is a good place…