Reflection #12

Well we have a test tomorrow and me matt and terrio are having a hardcore review right now.
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
Steps to Related Rates Problems.
-Identify all given quantities and quantities
to be determined. Make a sketch and label the
quantities, or Identify what you are given in the problem.
-Write an equation with the variables
whose rates of change are either given or are
to be determined.
-Using the Chain Rule, implicity differentiate
both sides of the equation with respect to
time t. Meaning rates will be (d__/dt)
-Last, substitute into the equation all the known values for the variables and their rates of change. Then solve for the rate of change you are asked for.
Ex:xy^3=3
dy/dt=?x=5 dx/dt=4
xy^3=3
3xy(dy/dt)+y^2(dx/dt)=0
3(50y(dy/dt)=y^3(4)
15y(dy/dt)=3y^2
dy/dt=4y^2/15y