33 and 34?

Well we have had a week off! But I guess it's back to school, so....

REMEMBER:
position
velocity
acceleration

A particle's position is given by s=t^3 - 6t^2 + 9t. What is its acceleration at time t=4? **When going down (from position to acceleration) you take the derivative. Then simpley plug in 4.
3t^2-12t+9
6t-12
6(4)-12= 12


REMEMBER:
related rates; sometimes we forget the steps

1. Identify all variables
2. Identify what you are looking for
3. Sketch & label that graph
4. write an equation using all of the variables
5. Take the derivative of this equation
6. Substitute everything back in
7. Solve


REMEMBER:
formulas; these problems are usually easy when you remember the formula

delta x=b-a/number of subintervals
LRAM-Left hand approximation= delta x[f(a)+f(a+delta x)+...f(b-delta x)]
RRAM-Right hand approximation= delta x[f(a+delta x)+...f(b)]
MRAM-Middle approximation= delta x[f(mid)+f(mid)+...]
Trapezoidal-delta x/2[f(a)+2f(a+delta x)+2f(a+2 delta x)+...f(b)]

volume of disks is S (top)^2-(bottom)^2 dx
area of washers is S (top)-(bottom)


REMEMBER:
implicit derivatives; has an = sign

y^3+y^2-5y-x^2=-4
1. take derivative of both sides:
3y^2(dy/dx)+2y(dy/dx)-5(dy/dx)-2x=0
*remember every time you take the derivative of y, you have to note it by dy/dx or y^1
3. solve for dy/dx: (you are going to have to take out a dy/dx when solving)
3y^2(dy/dx)+2y(dy/dx)-5(dy/dx)=2x
dy/dx(3y^2+2y-5)=2x
dy/dx=2x/3y^2+2y-5
*Also, if you want the slope you must plug in a x and y-value.


REMEMBER:
key word stuff; when you see a word you should immeditaly think..

1. linearization-->equation of a tangent line
2. if given a table(the sets of points)-->dealing with slope or rram/lram/ect.
3. how many-->integrate
4.(in calculator part)volume problems-->find intersection


AND REMEMBER:
slope field stuff; we are fixing to start with more free response

I'm just going to review how to draw it.
positive slopes is /
negative slope is \
for a zero slope is a horizontal line
for an undefined slope is a vertical line


*Oh and we take a real ap test tomorrow! I almost forgot..good luck.