1. More Index cards for AB

2. Separation of Variables
The steps with an example

3. Step 1: separate the y dy on the left and the x dx and other stuff on the right
Step 2: integrate both sides. Remember the + C
Step 3: solve for c using the initial conditions
Step 4: solve for y

4. Linear approximation or Use the line tangent to approximate an answer

5. Linear approximation or Use the line tangent to approximate an answer
Find the slope (derivative)
Construct the line tangent using a given point or a point close to the approximation
Plug in x that you are trying to approximate and solve for y

6. The derivative of

7. The derivative of

8. Inverse Functions
Some notes: all about switching the x and the y. Denoted
Example: If g has a point (2, 5) or g(2)=5, where the slope is 3/7
Then find f(5) =, and the slope at f(5)

9. Inverse Functions
f(5) = 2, and the slope at f(5) is 7/3

10. Differentiable functions
Of these graphs, which are differentiable at c and which aren’t
If a function is differentiable, then it has to be _____________

11. Differentiable functions
If a function is differentiable, then it has to be _continuous__

12. The Rules

13. How I do word problems 1. Read the problem once to get a general idea
2. Read it again and start drawing a picture and writing down information.
3. Try some easy numbers to figure out relationships. Then write down equations you are using in general form.
4. Analyze what they want you to find. Largest, biggest etc is a max, smallest is a min. This is the equation that you will be derivatizing (made-up word).
5. Find where the derivative = 0. When you find solution, read the last sentence again. What do they want?

14. Solving related rates 1. Read it through once
2. As you read it through the second time, draw a picture and write down the important info.
3. Analyze what we have, what we need to find
4. Write an equation that relates the info
5. Take the derivative with respect to t and substitute the info into the derivative equation