Sunday, September 20, 2009

post 5

after the fifth week of calculus im pretty confused on some things. i know the first and second der tests pretty well. i know how to get the maxes and the mins which has to do w/ the first der test and i know the concave up and down which has to do w/ the second der test. we also have to justify all the answers we get. the justifying thing is what is kind of hard to do. i'm not really goodd at explaining myself in math talk haha the first and second der tests are what im pretty goodd at.
here is an example problem of max andd min.

Find the absolute MAX/MIN of f(x) = 3x^4 - 2x^4 on [0,3] :

First, take the derivative. 12x^3 - 8x^3
Set equal to zero, find critical values and endpoints, plug in for x to find y values, smallest = min ; largest = max
you need to put the max and min in point form.

im not too sure of drawing the graphs when the information is given. i knonw the points of discontinuities and what they look like on teh graph. i know how to find them when given an eqn as well. i dont know differtiability too much so if anyone wants to help comment me
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2 comments:

  1. ryan.is.in.calc.September 22, 2009 at 8:15 PM

    One thing about the graphs is switching from the original function to the first derivative graphically. To do this you take all the relative maxs or mins on the orginal and they will be x-intercepts. Then you look where the graph is increasing or decreasing. Where it is increasing, the first derivative graph will be above the x-axis. Where it is decreasing, the first derivative graph will be below the x-axis.

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  2. MamieSeptember 23, 2009 at 10:02 PM

    When you have a word problem and/or a graph and you have to draw either the first derivative of the origional function graph or the origional function graph when given the first derivative, you have to find the key things you are looking for.

    For example, if you are looking at a graph of an origional function and it has zeros at -4, 0, and 4; on the first derivative graph of the function, your zeros will always become your maximums and mimimums. This works both ways.

    If on your first derivative graph, you have zeros on the x intercept, they will be the maximums and minimums on your origional function graph.

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