As I announced in class, will have our **first midterm exam (Exam #1) on Wednesday October 9**. See below for a list of topics and exercises to to review.

Included are exercises from the “Derivatives – Power Rule” Webwork. We will discuss some of those exercises in class on Monday, but work through as many of those exercises as you can on your own.

**Topic**s

The main topics we have covered so far this semester and which will be covered on the exam are:

- the limit definition of the derivative
- finding the equation of a tangent line at a given point (using the derivative to find the slope), and sketching such a tangent line for a given graph/point
- the differentiation rules

For **the limit definition of the derivative**, you can review:

- Sec 3.1: Examples 3.1, 3.3, 3.6
- WebWork – “Derivatives – Limit Definition”: #3
- Sec 3.2: Examples 3.12
- “Derivatives – Functions”: #2 & #3 (see Class 8)
- Quizzes #1 & #2

You should also understand this figure (Fig 3.3 from Sec 3.1 — similar to the graph I had you sketch for HW#1, which I will return on Monday), and how it leads to the limit definition of the derivative:

**Differentiation rules:**

**Finding the equation of a tangent line** at a given point (using the derivative to find the slope, and then using the point-slope equation of a line), and **sketching a tangent line** for a given graph/point:

- Look in your class notes/Class Recaps for when we have sketched tangent lines for graphs; see also these two Desmos graphs where we plotted tangent lines (here and here)
- See again Examples 3.1 & 3.3 in Sec 3.1, and “Derivatives – Functions” #2
- “Derivatives – Power Rule”: #14-15
- Sec 3.3: Example 3.22
- Explanation and example at start of Class 5, using the function from Quiz #1 (see also this related Desmos graph)
- You should also understand what
**a horizontal tangent line**looks like, and how you can solve for the points where a graph has a horizontal tangent line (i.e., by solving the equation f'(x) = 0)- See “Derivatives – Power Rule”: #16 & Example 3.31 in Sec 3.3

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