Per the request of a student in class, I am providing a study guide for the upcoming quiz in class. First, I will share the standard and the learning objectives and try to break that down and provide examples.
EU 2.1 – The derivative of a function is defined as the limit of a difference quotient and can be determined using a variety of strategies.
- LO 2.1A – Identify the derivative of a function as the limit of a difference quotient.
- LO 2.1B – Estimate derivatives.
LO 2.1C – Calculate derivatives. LO 2.1D – Determine higher order derivatives.
We are really only assessing half of the standard right now and leaving the second half for later in the unit. You will need to be able to:
- Use the difference quotient (limit definition) of the derivative to compute the slope of a tangent line at a specific point
- Understand notation f'(a) and dy/dx as notations communicating a need for a derivative.
- Use a graph to estimate the derivative of a function based on the image provided (no equation provided for the function).
- Estimate (assuming a function is continuous) the derivative based on tables and graphs.
Here are some video resources from to support learning that may have been missed in class:
- Concept of a Derivative
- Secant Lines vs. Tangent Lines (Average Rate of Change –> Instantaneous Rate of Change)
- Derivative Notation (Practice Set)
- Derivative as Slope
- Limit Definition of Tangent Explained
- Estimating Limit from a Table of Values