Sunday, April 18, 2010

post 35

LINERAZATION
The steps for working linearization problems are:
1. Identify the equation
2. Use the formula f(x)+f ' (x)dx
3. Determine your dx in the problem
4. Then determine your x in the problem
5. Plug in everything you get
6. Solve the equation

LIMIT RULES
The limit rules are:
1. if the highest exponent is the same on the top and bottom then the limit is the top coefficient over the bottom coefficient of the highest exponents.
2. If the highest exponent is on the top then the limit is infinity.
3. But if the highest exponent is on the bottom then the limit is 0.

RELATED RATES:
The steps for related rates are:
1. Identify all of the variables and equations
2. Identify the things that you are looking for
3. Sketch a graph and then label that graph
4. Create and write an equation using all of the variables
5. Take the derivative of this equation with respect to time
6. Substitute everything back in
7. Solve the equation


First derivative test:

For the first derivative test, you are solving for max and mins and may be trying to see where the graph is increasing and decreasing. You take the derivative of the function and and set it equal to zero and solve for the x values (critical points). Then you set those points up into intervals between negative infinity and infinity. Then, you plug in numbers between those intervals to see if it is positive or negative.

Second derivative test:

For the second derivative test, you are solving to see whether the graph is concave up, concave down, or where there is a point of inflection in the graph. You take the derivative of the function twice and set it equal to zero and solve for the x values. You set those values up into intervals between negative infinity and infinity. You then plug in numbers between those intervals to see if it is positive or negative. If it is positive, it is concave up. If it is negative it is concave down. Where there is a change in concavity, there is a point of inflection.

I dont remember optimization. help
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2 comments:

  1. gonzoApril 19, 2010 at 6:55 PM

    my favorite optimization:

    1 Identify primary and secondary equations your primary is the one your or maximizing or minimizing and your secondary is the other equation
    2. Solve for your secondary variable and plug into your primary equation if your primary only has on variable this isn�t necessary
    3. Plug into secondary equation to find the other value check your end points if necessary

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  2. jessieApril 21, 2010 at 8:25 PM

    OPTIMIZATION!:
    1. Identify primary and secondary equations. Primary deals with the variable that is being maximized or minimized. The secondary equation is the other one.
    2. Solve the secondary equation for one variable
    3. Plug ^that variable back into the primary. If the primary equation only has one variable you can skip this step.
    4. Take the derivative of the primary equation after plugging in the variable
    5. Set it equal to zero and solve.
    6. Plug that variable back into the secondary equation in order to solve for the last missing variable.

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