post 25

time for some calculus before the super bowl yeeerrrrrrrrrrrdddmeeeeeeeeeeee

maxs and mins:
1. Find critical values by using the first derivative test: take the derivative set equal to zero and solve for the variable.

2. Plug both intervals as well as the critical values into your original equation

3. Be sure to keep the value after substitution with each appropriate number.

4. To determine which constitute a max and which constitute a min, you must look and point out those of which have the lowest values-min- and those of the highest value-max.

Substitution takes the place of the derivative rules for problems such as product rule and quotient rule. The steps to substitution are:
1. Find a derivative inside the interval
2. set u = the non-derivative
3. take the derivative of u
4. substitute back in

linearization.

The steps for solving linearization problems are:
1. Pick out the equation
2. f(x)+f`(x)dx
3. Figure out your dx
4. Figure out your x
5. Plug in everything you get

implicit derivatives:

First Derivative:
1. take the derivative of both sides
2. everytime you take the derivative of y note it with dy/dx or y^1
3. solve for dy/dx

Related Rates:

1: identify all variables in equations
2: identify what you are looking for
3: sketch and label
4: write an equation involving your variables. (you can only have one unknown so a secondary equation may be given)
5: take the derivative with respect to time.
6: substitute derivative and solve.


Infinity rules:

1. If the degree of the top is greater than the degree of the bottom, then the limit is going to infinity.

2. If the degree at the top is less than the degree at the bottom, then the limit is going to zero.

3. If the degree of the top is the same as the degree of the bottom, set the
coefficients to a fraction.

some things i'm not too good w/ is slope fields, e integration, and lram rram and mram.