Ok. So the beginning of the week was hectic in terms of preparing for the test and such. Going into the test, I thought that I was doing good. I knew all of my derivative formulas and could work out problems to the best of my ability, I think. However, even though I knew that limits would be on the test, I was not nearly prepared as I thought I was for that portion. I understand how to find finite and infinite limits, but I totally do not remember how to do the right and left hand limits (that would be my major question ???).
On Thursday when Ms. Robinson introduced to us all the of the vocabulary for the graphs, I was a little freaked out. I kept copying down all the stuff on the graphs, but couldn't really grasp it, that is, until Friday.
So, I after doing all the examples I finally got it, and the grouping of the terms kind of helped me as well. This is the way I remember it:
Original: Increasing, Decreasing, maximum, minimum.
1st derivative: Positive slope, Negative slope, horizontal tangent
2nd derivative: Concave up, Concave down, point of inflection.
And then we have how they're all related:
(Increasing, Negative slope, Derivative below the axis, concave up.)
(Decreasing, Positive slope, Derivative above the axis, concave down.)
(Zero of a derivative, Horizontal tangent, minimum.)
For me, I had to see the graph to do this at first, but then on Friday we also went into doing the first derivative tes (KEEP IN MIND: FIRST derivative).
Steps are as follows:
1. Take the derivative
2. Set = 0
3. Solve or x =>max & min (extrema), horiz tangent
4. Set up intervals using step 3
5. plug in 1st derivative
6. To find an absolute max/min plug values from #5 into original function. Check endpoints.
So, that's all I have and if someone could review the whole right left hand thing for me, it would be greatly appreciated!
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ReplyDeletethis was supposed to be post #3....my bad!
ReplyDeletei think for right and left hand limits, if you are given a graph, and say you are finding lim x->2+ you cover up the left hand side and see where the graph is approaching at 2. If you are looking for 2-, you cover up the right hand side and see where the graph is approaching.
ReplyDeleteIf they are approaching the same number, that is the limit. If they are approaching a different number, the limit does not exist.
For the left and right side limits that you're confused about, i think you just go to the graph. When it is something like 4- you cover up the right hand side of the graph and look for where the graph is going as it is approaching 4. Then for 4+ you cover up the left side of the graph and see where the graph is going as it approaches 4. If what you get for those two sides do not equal, the limit does not exist whereas if they do equal the limit is at that point.
ReplyDeleteLol, to further explain the left and right hand side thing...in a bit different way.
ReplyDeleteThe reason that you cover up the right hand side when you look for 2- is because the negative tells you to look on the negative side of the graph. 2- is to the left, 2+ is look to the right.
So for 2- cover up the right so you can only see left and for 2+ cover up the left so you can only see the right.
Not sure why we never explained it this way. Makes more sense to me. Might just be me though.
i always just thought if it was a - you cover up the right, and if it's + you cover up the left. but the way it was just explained was really good. thanks dude, that helped me too.
ReplyDeleteI am pretty sure when I first introduced it I explained it that way with a number line. However, after that I revert to the proper terms so maybe next year I will reiterate that several times...
ReplyDelete