post 37

Well the ap test is really close and I so need to study!

Optimization:
1. Identify all quantities
2. Write an equation
3. Reduce equation
4. Determine domain of equation
5. Determine max/min values


substitution:
1. Find u and du
2. set u equal to whatever isn't the derivative
3. take the derivative of u
4. substitute back in


LRAM- left hand approximation x[f(a)+f(a+x)+...f(b)]
RRAM- right hand approximation x[f(a+x)+...f(b)]
MRAM- approximation from the middle x[f(mid)+f(mid)+...]
Trapezoidal- x/2[f(a)+2f(a+x)+2f(a+2x)+...f(b)]


average rate of change:
just a slope; f(b)-f(a)/(b-a)


linearization:
1. Pick out the equation
2. f(x)+f`(x)dx
3. Figure out your dx
4. Figure out your x
5. Plug in everything you get


slope field stuff from free response:
(what to draw)
positive slopes is /
negative slope is \
for a zero slope is a horizontal line
for an undefined slope is a vertical line

I sometimes just mess up on taking the derivative or integrating wrong. Any tips for integration?