We learned a lot this week.
On Monday we learned how to find the second derivative (d^2y/dx^2) of implicit derivatives. The only difference between this and regular implicit derivatives is that you first of all take the second derivative and where dy/dx ends up in the second: plug in what you got for the first.
On Tuesday we learned about Related Rates.
Steps for finding the Related Rate:
Identify all variable and equations.
Identify what you are looking for.
Make a sketch and label.
Write an equation involving your variables. Know that you can only have one unknown variable, so a secondary equation may be given.
Take the derivative with respect to time. aka: (dy/dt) or (dx/dt).
Substitute in derivative and solve for the rate.
We also worked a problem that Ms. Robinson said would be on the AP exam, so make sure you make note of it. It was the concentric circles in the pond example.
On Friday we did a problem on Angle of Elevation that I did not understand.
It was: Find the rate of change of the angle of elevation of the camera in the figure 10 seconds after life off. If the rocket is rising according to the position equation y=50t^2.
I also do not understand any of the word problems relating to the Related Rates. Can someone maybe explain this to me?
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Related rates are kind of like optimization.
ReplyDelete1. Identify all variables and equations
2. Identify what you are looking for
3. Make a sketch and label
4. Write an equation involving your variables
5. Take the derivative with respect to time
6. Substitute in derivative and solve.
Basically, identify what's given and what you're looking for.
ReplyDeleteDraw a picture.
Make an equation (usually area, volume, pythagorean theorm).
Take the derivative. Plug in and solve ^^
Hope this helps!
Don't forget, repitition helps a lot too!