I find I still have a major problem with simplifying. I tend to cancel things that do not cancel or if I have cos x + sin x and I have to set it equal to zero I separate the two and set each equal to zero which I know I can't do but I still accidentally did it three times on the take home tests, that only works if you're multiplying by the way. I also am having trouble going from and equation to a graph especially numbers 1 and 2 on 3.6. I understand how to find the relative extrema, points of inflection, intercepts and asymptotes, but I do not know how to actually form a graph from the information I find.
The thing I am most comfortable with and I think I fully understand is first and second derivative test but since a lot of people explained that I am going to take a stab at explaining the relationship between the original graph and the first derivative graph because I feel I have gotten better at it over the course of this week.
If you are giving an original graph of f(x) and are asked to find the critical numbers, they are just the maxs and mins of the graph.
If you are asked to find the zeros, it is everywhere the graph crosses the x-axis.
If asked to find the zeros of f'(x) it is the maxs and mins of the original function (the same as the critical numbers) because when you sketch the derivative you move the maxs and mins to the x-axis.
If the original graph is increasing, the f' will be above the axis but if the original is decreasing f' will be below the axis.
This may seem easy but I think we learned this about two weeks ago and I finally just caught on for the most part this week. It really helped me with trying to do the study guide so I hope it helps yall too.
just a tip for simplifying. It's a lot easier if you just take it slow and go one step at a time. Like brob said, the first thing you see, or the biggest thing, is what you do first. In other words, work from the outside in.
ReplyDeletealso, you were right about the setting equal to zero thing for sin(x) + cos(x). ryan gonzalez always gets confused on that too, haha. you set the whole thing equal to zero unless you are multiplying. like if you had sinxcosx + sin^2(x). then you would factor out a sinx. sinx(cosx + sinx). Then you would set sinx = 0 and cosx + sinx = 0.
Hope this helped :)
i think the easiest way to remember it is to work from outside in and if you have a plus sign, you're screwed. Plus signs eliminate a lot of potential cancelling..
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