3rd Post

This week in Calculus started off with two days of reviewing. We took a test on Wednesday. I believed I was ready for the test until I saw it and then realized that I was not prepared. Thursday and Friday we learned new concepts that are seemingly simple with many things to remember. We learned many new terms of vocabulary words and other ways to define words we knew from previous years of math.

Some of the terms we learned were increasing, decreasing, concave up, concave down, and positive and negative slopes. These terms just about explain themselves. For example, if a slope is positive it is increasing; if the graph is increasing, it’s positive. Also, if a slope is negative it is decreasing; and if it’s decreasing, it is negative.

I understand the basic concepts and definitions of this but I do not understand how to work a problem with it. I understand that slope is positive when the graph is concave up, and negative when the graph is concave down. Also, when the graph is above the x-axis, your interval would be from zero to infinity and below the x-axis intervals would be from negative infinity to zero. Maximums and minimums were also discussed this week. I realized that max and mins are only new words to describe increasing or decreasing points in a graph.

Also, we learned about taking the first derivative test. I only understand the rules, and can almost follow them but I get confused with my graphs. To take the first derivative, you must take the derivative of the equation, set it equal to zero, solve for x. After you solve for x, you will have the maximum, minimum, horizontal tangents, and extrema. If the problem asks you to step farther, you then set up intervals and plug in the first derivative into the equation. Next, plug values in from the intervals into the original equation to find the ABSOLUTE maximum and minimums. The last step would be to check your endpoints.

This is really the only thing I can explain. I can’t put it into a problem, because I get confused when that happens. I could really use someone just taking it step by step with the graphs. I don’t get confused until the graphs come along…which is kind of the whole problem. So I think I’m in trouble. If anyone can help me understand the graphs it would be appreciated.