Students examine the foundational components of limits, derivatives, integrals, and series and apply this knowledge to real-world situations. Derivatives are used to find slopes of lines tangent to curves at specified points. Students learn specific rules of differentiation and explore real-world applications, including related rates and optimization. Students explore the graphs of functions and their first and second derivatives to reveal the functions’ characteristics. Functions increase in complexity to include logarithmic and exponential components. Integrals are explored as various methods of finding the area under a curve are examined and applied, and each method is supported graphically. Integration is used to revolve solids about an axis. At the conclusion of the course, students learn about series, including Taylor and Maclaurin series, as well as how to prove convergence or divergence using integral and p-series tests.
Tangent and normal lines
Derivative rules and notation
Derivative applications Chain rule
Derivatives of inverse functions
Graphs and derivatives
Interpret limits, continuity, and discontinuity given an equation or graph.
Apply rules of differentiation to find the derivative of a function.
Explain the connection between the derivative and identifying the velocity, acceleration, and jerk. Apply the rules of differentiation to inverse functions.
Identify how the rate of change of a function affects the rate of change of individual components.
Utilize the derivative to identify key elements of graphs.