Sunday, March 21, 2010

Post Number Thirty One

Almost doneeeeeeeeeeeeeeeeeeeeeeeeeeeeeee with school.
All these weeks of aps and I’m finally starting to do a little better, hopefully it stays improving..

Implicit derivatives are pretty easy.
1.Take the derivative of both sides like you would normally do
2. Everytime the derivative of y is taken it needs to be notated with either y ' or dy/dx
3. Solve for dy/dx or y ' as if you are solving for x.

I finally remembered mean value theorem on the last test!
If f is continous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a number c in (a,b) such that F'(c) = f(b) - f(a) / b-a

Related rates..i know the steps but can someone work a problem for me?
1.Identify all variables
2. Identify what you are looking for
3. Sketch & label that graph
4. write an equation using all of the variables
5. Take the derivative of this equation
6. Substitute everything back in
7. Solve

I need help with tangent lines, normal lines, definition of a derivative, deciphering between graphs of derivatives, instantaneous speed….
Etc etc

Limit rules for the limit approaching infinity
1. if the degree of top equals the degree of bottom, the answer is the top coefficient over bottom coefficient
2. if top degree is bigger than bottom degree, the answer is positive or negative infinity
2. if top degree is less than bottom degree, the answer is 0

Goodnight calculus!
One 9 weeks left!
Oh lehhhh do it

5 comments:

  1. for the definition of a derivative
    if you have a number then you plug it in, but if you just have a variable you take the derivative [you always look at the last part on top of the equation given]
    FOR EXAMPLE:
    h-0 sinx^2+x
    since there is no number to plug in for x
    you just take the derivative:
    2sinxcosx+1
    HOWEVER:
    h-0 ln2
    since there is the 2 there then that's what you plug in after you take the derivative:
    1/x is ln
    so now plug in 2 for x giving you 1/2
    HOPE THIS HELPS!

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  2. For tangent lines, you take the derivative of your function and plug in x to get your slope. Once you have that, plug your x, y, and slope into point slope form and you'll have your equasion.

    For normal lines, you do the same thing to find your slope except you take the negative reciprocal of it and use that as your slope.

    For graphs, when you're looking at a graph of f'(x)and they're asking about f(x) just remember that your makes and mins on the graph you are looking at are going to be your zeros on f(x) and the zeros you are looking at on f'(x) are going to be maxes and mins on your f(x) graph. Also, to decipher between what's a max and what's a min, you look at to see where it is negative and positive. If a graph goes from negative to positive, it is a minimum; if it goes from positive to negative, it is a maximum.

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  3. tangent lines- take the derivative of your function and plug in x to get your slope. then plug your x, y, and slope into point slope form and you'll have your equation.

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  4. normal lines:

    take the derivative, find the slope, take its inverse, then plug it into point slope form

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  5. The only thing to add to Ellie's explanation of the definition of derivatives is: Do. Not. Take. The. Limit.
    That usually gets me, making me spend a lot of time on useless plugging in, when I could be taking the derivative of usually one part of the equation (first part at the top) and then plugging in zero!
    Very simple after you get the hang of it =]

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