post 33

Well the holidays are over and its time to get ready for the AP test so I will start by going over some old things.

The steps for the first derivative test are:

1. Take the derivative of the original function

2. Solve for x (the values will be your critical values)

3. Set those values up into intervals between negative infinity and infinity

4. Plug in numbers between the intervals into the function

5. This will show you when the function is increasing, decreasing, and you will find max's and mins

The limit rules are:

1. if the degree of the top is bigger than the degree of the bottom, the limit is infinity.

2. if the degree of the top is smaller than the degree of the bottom, the limit is 0.

3. if the degree of the top is equal to the degree of the bottom, the limit is the coefficient of the leading term of the top divided by the coefficient of the leading term of the bottom equation.

The steps for optimization are:
1. Identify all quantities
2. Write an equation
3. Reduce equation
4. Determine domain of equation
5. Determine max/min values

The steps to find maximums and minimums are:
1. First derivative test
2. Plug critical values into the original function to get y-values
3. Plug endpoints into the original function to get y-values
4. The highest y-value is the absolute maximum
5. The lowest y-value is the absolute minimum


The steps for related rates are:
1.Pick out all variables
2. Pick out all equations
3. Pick out what you are looking for
4. Sketch a graph and label
5. Create an equation with your variables
6. Take the derivative respecting time
7. Substitute back into the derivative
8. Solve