Post Number Thirty Three and Post Number Thirty Four

These are my blogs for spring break, I think 33 and 34..

Hope everyone had a great Easter!

I finally remembered Mean Value Theorem:
F(x) must be continuous on a closed interval and differentiable on the open interval.
f '(c) = [f(b) - f(a)] / (b-a)

Optimization:
1. Identify all quantities
2. Write an equation
3. Reduce equation
4. Determine domain of equation
5. Determine max/min values

Finding absolute max/min:
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

Volume by disks:
Pi bSa [R(x)]^2 dx

Volume by washers:
pi bSa (top equation)^2 – (bottom equation)^2 dx

After doing the substitution worksheet the other day, I finally feel more comfortable:
1. Find a derivative inside the interval
2. set u = the non-derivative
3. take the derivative of u
4. substitute back in

Limit Rules:

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.

Although I know the steps for related rates I always get mixed up during the problems:
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

PVA
Remember, it goes down. Moving down the list, take a derivative, such as changing from position to velocity. Moving up the list, integrate, as if changing from acceleration to velocity. If going from position to acceleration, take the derivative twice. If going from acceleration to position, integrate twice.
Easy enough, right?

First derivative test:
-Take the derivative of the original function
-Solve for x (the values will be your critical values)
-Set those values up into intervals between negative infinity and infinity
- Plug in numbers between the intervals into the function
-This will show you when the function is increasing, decreasing, and you will find max's and mins

Second derivative test:
-Take the derivative of the original function twice
-Solve for x values(critical values)
-Set up into intervals between infinity and negative infinity
-Plug in values between the intervals into the function
-This will show you where the graph is concave up and down, and where there is a point of inflection.

Although I know what to do a lot of times, I have a lot of trouble putting my knowledge to use. I often get mixed up and lost in the middle of problems and don’t know what to do next. Some things I guess I’ll just never understand.
Oh and I won’t be in class tomorrow, so let me know what goes on!