This week was alright i guess, we had a sub on thursday and friday, but i was out thursday and friday i worked on the take home test which by the way is extremely difficult!!! I did alot of related rate problems so ill talk about this.
1. Identify all given quantities and quantities
to be determined. Make a sketch of the problem and label the
quantities correctly.
2. Write an equation involving the variables
whos rates of change either are given or are
to be determined. In other words, list what you KNOW, and list what you are TRYING TO FIND.
3. Using the Chain Rule, implicity differentiate
both sides of the equation with respect to
time t. (this means that all rates will be d something/dt
4. After completing Step 3, substitute into the
resulting equation all known values for the
variables and their rates of change. Then
solve for the required rate of change.
Key words to look for are: Cubic = looking for volume; the rate of = d something/ dt
Example:
xy = 6
Step 1: dy/dt = ? x = 4 dx/dt = 8
Step 2: xy = 6
Step 3: xdy/dt + ydx/dt = 0
Step 4: xdy/dt = -10y
= -2y
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