alright, so i'm not too sure if this is supposed to be easy or not, but it definitely is not easy for me. I missed one day of school, i'm not sure which day, but i missed the Rolle Theorem lesson. So i have absolutely no idea how to do that section of the chapter. If anyone can comment to help explain, then i might not fail the test when we have it. But i can try to explain the notes and maybe it will help me learn.
Rolle Theorem:
1. Make sure it is continuous.
2. Make sure it is differentiable.
3. Make sure the y-values match.
4. Take the derivative, set = 0, and solve for x.
*You use Rolle Theorem when trying to find a max or a min, or trying to prove that there is a max or a min.
Mean Value Theorem:
*Set derivative = to slope between two points and there has to be a value x you can solve for if it is continuous and differentiable on the interval.
First Derivative Test:
1. Take derivative = 0.
2. Find where it is not differentiable.
3. Set up intervals using step 1 and 2.
4. Plug in a number on the interval into the original equation.
5. If positive, it is increasing, if negative, it is decreasing.
6. Determine max or mins from step 5. Increasing/decreasing - max; Decreasing/increasing - min.
*critical points= step 1&2
*extrema,max,min,inc.,dec.,= all 6 steps
Well that is all we learned for the entire week, and i think i understand most of it. But more practice will surely help. It is much easier when we are working problems in class.
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