The thing i understand the most in calculus this week is absolute maximums and minimums. To do this, you simply follow simple steps:
1. first derivative test
which consists of:
Take Derivative
Set Equal to Zero
Set Up intervals
2. plug the critical values into origional function to get y-values
3. plug endpoints in to origional function to get y-values
4. your highest y-value is absolute max
5. your lowest y-value is absolute min.
**absolute maxs or mins or written as a point or simply as the y-value.
These problems are extremely simple to solve because it only involves simple algebra. Just remember, when the graph becomes discontinuous. Jumps only occur when you have a peicewise function. You find removables by factoring the top and bottom of your function..if something cancells out then its a removable at x=whatever that number is. Then after you cancel, if you have anything left at the bottom you have an infintite(asymptote) at that number. These are reallly easy to do, as long as you remember when the discontinuities occur. Remember these simple formulas, and your set for life. :)
The thing I do not understand this week is still the graphs. I do not understand how to take a graph and determine how to take the second derivative, or the first, or original function. I know what the graph will look like, but not where it is on the graph. Please help me because i'm pretty sure it will be on the test tomorrrowwwww.
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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. And going between the first derivative and the second derivative is the same thing.
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