pos #1 holidays

i can't tell you how glad i am to be on vacation, i don't think i could take another week of school right now! thank youuu christmasss!

lets go over related rates because i still need a review.

1. Identify all your variables and equations. Some may be given
2. Identify what you need to solve for.
3. Make a sketch or draw a picture of what you are given
4. Take the derivative of the equations with respect to time.
5. Plug in given numbers to the derivative and solve.

EXAMPLE 1: This problem has the equation and given information.


x^2+y^2=25 dy/dt when x=3, y=4 dx/dt= 8

Derivative: 2x dx/dt + 2y dy/dt= 0

When you plug in you get: 2(3)(8) + 2(4) (dy/dt) = 0

48+ 8 dy/dt=0
dy/dt= -6


mmm.. now how about implicit derivatives.

STEPS:
1. Take the derivative.
2. For each y-term, you put y' or dy/dx behind it.
3. Solve for dy/dy or y'.

36x^2 + 2y = 9
36x + 2(dy/dx) = 0
2(dy/dx) = -36x
-36x/2
dy/dx = -18x

HELLLP? i still don't unederstand optimiazation from way back in the gap so if anyone wants to show me go for it, thanks. MERRYY CHRISTMAS!