So at the beginning of this week we didn't learn many new things. We just added onto old things and worked problems on them. We worked problems that included using the frist derivative test, the second derivative test to find points of inflection, where a graph concaves up or down, and a shortcut way to find maximums and minimums; however, we can only use these shortcuts on multiple choice and when a short answer question asks for it. We were given an assignment to find a career that involves math. The new material we covered was how to find absolute maximums and minimums, which are either the highest point of all high points, which would be the absolute maximum, and the lowest point of all low points, which would be the absolute minimum.
To find the absolute maximums and minimums the steps are as follows:
1. First derivative test
2. Plug critical values into the origonal function to get y-values
3. Plug endpoints into the origional function to get y-values
4. The highest y-value is the absolute maximum
5. The lowest y-value is the absolute minimum
*Remember that absolute maximums or minimums are written as a point, or simply as the y-value
After this, we were pretty much given the whole week to review on different types of problems covering everything from when we started out the school year, all the way down to finding the absolute maximums and minimums.
I understood how to read and graph origional function graphs, first derivative graphs, and second derivative graphs much better after I got together with a few classmates who were willing to help me understand them on Wednesday. Before this study session, I really didn't understand the concept that if the origional function graph was decreasing, that its first derivative would be starting below the x axis and if the orgional function graph was increasing, that its first derivative would be starting above the x axis. I also learned that when there is a zero on an origional function graph, the zero will become the maximum or minimum on the first derivative graph, and vice versa.
I feel very accomplished this week after completing all the things I've completed and I really feel greatful for the people who've helped me complete these things.
The only real question that I have is how to graph a tangent line. I've asked this question before and I've learned it time and time again, but I keep on forgetting. Can someone please explane?
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I'm not sure if I understand what you mean by "Graph" a tangent line. A tangent line is simply a straight line that is perpendicular to the graph at a certain point...
ReplyDeletehttp://mathforum.org/cgraph/history/pictures/glossary/tangent.gif
That is an example of a tangent line.
Perhaps you meant how to find one? If that is the case, you find the slope that you want it to be parallel to. You then take the derivative and set it equal to that slope. Solve for x, plug in that x into the original function to get a y. Now you can use the slope, the x and the y and plug into point-slope form to find the equation of the tangent line.
If you need more help with this just let me know at school or something and I can explain it a bit better.
you don't graph a tangent line. you only find one on a graph or in an eqn
ReplyDeleteYou said you don't know how to graph a tangent line but we were never asked to graph it i don't think.
ReplyDeleteYou just have to find it.
In order to find it you first take the derivative and set it equal to the slope you want the line to be parallel to. after doing so you solve for x. Plug in the x into the original function to get your y. After getting all of these things you simply plug into point-slope form, giving you the equation of a tangent line :)