whew... well this week was a difficult week for me in calculus but luckily we had a study group yesterday at PJ's and i understand some of the concepts better than what i did before. First of all, absolute max and mins are very easy. First you take the derivative of the original function and set it equal to zero. Then you find your critical points and set up intervals. Then you plug in your critical points and endpoints into the original function. Your biggest y value will be your absolute max and your lowest y value will be your absolute min. Another concept i understand better is finding the slope of a line with a given function and x value. You take the derivative of the function and then plug in the x value to get the slope... super easy :).
What i'm not so sure about is how to draw different graphs when the problem gives you different information. If the function gives you a critical point say 5 and they say no extrema or stuff like that, i do not know how to draw that. If someone can explain how to do that it would help a lot. Another thing i'm still not sure about is looking at the graph and figuring out what the derivative form of the original function is supposed to look like or vice versa. So for example if they give me a graph and show a line going through a number on the x axis and they want to know what the first derivative of that graph is supposed to look like, i do not understand what the graph is supposed to look like and if there are certain things that i should be looking at to get the answer. If anyone can help me understand what to look for it would be a great help. Thanks :)
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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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