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