So, Tuesday and Wednesday wasn't bad at all...I thought I knew was I was doing. The worksheet wasn't bad and the vocabulary didn't seem hard to understand and write in my own words either. Then Thursday came, I went to Tulane because I was chosen out of the Senior class to tour the school we could most likely have an opportunity to attend one day. I ended up having to miss class, WHICH SUCKS btw, making it really hard to understand what we did Friday.
Friday, I'm guessing that we "continued" to learn what Mrs. Robinson taught on Thursday. We did learn the Second Derivative Test. There are points of inflection, intervals of concavity [concave up/concave down], and shortcut for MAX & MIN. She said, "Beware, points of inflection only happen if there is a change in concavity." An example problem would be:
x^2 + 1
----------
x^2 - 4
since that's the original, we need to first find the first derivative:
(x^2 - 4) (2x) - (x^2+1) (2x)
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(x^2-4)^2 which gives you...
-10x
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(x^2-4)^2 for the first derivative....now we have to take another derivative from this in order to find the second derivative...
(x^2)^2 (-10) -- [(-10x)2(x^2-4)(2x)]
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(x^2-4)^4 giving you....
-30x^2+40
---------------
(x^2-4)^3 which, simplified, will give you...
10(3x^2+4)
----------------
(x^2-4)^3 for the second derivative!!
your points of discontinuity is plus or minus 2 [from your original...take the bottom and set equal to zero and solve]. which means from (-infinity, -2) it's concave up, from (-2,2) it's concave down, from (2,+infinity) it's concave up. Another way of writing it is....concave up: x<-2 x>2......concave down: -2
To be honest...I really don't understand this. First off, taking the derivative...I always get something mixed up so I get it wrong, screwing my whole problem up. I wish there were simple terms to put it in, in order to make me understand, but I just can't get it. I know the formulas, so I'm not sure what I'm doing wrong, probably simple algebra...which btw isn't so simple!! Second, once I get the derivative of the first, the second derivative...which is like the same way...is just harder to do :(
But I do understand when it's concave up and down and all the rest of those vocabulary words. Oh but wait, how do you get that if you have just a problem...like on the homework...number 9...
1
----
x^2 it says to identify the open intervals on which the function is increasing or decreasing. So do I just take the derivative and find the points of discontinuity, then plug into the original...so see if it's increasing or decreasing...and since it's increasing/decreasing..isn't it just .. I only have to take the first derivative?
I'm pretty lost, and I don't like this...I try to ask questions in class, and it just doesn't seem to work or help!
--Ellie
Ellie,
ReplyDeleteIt is called the first derivative test. You plug into the first derivative to find out if it is increasing or decreasing. Friday was new stuff to everyone. It was not a continuation from Thurs. With the exception that we talked about how to write a justification at the end of a problem.
Oh and the homework is the same stuff you did in class on tues and weds. It has nothing to do with friday except you have to write a justification for each problem. So if you did ok on Tues and weds then you should be fine with the hw.
ReplyDeletefor the justification part..that's just basically writing out what i did in words right?
ReplyDelete