yo yo yo.
we took 2 ap's this week, except it was... OUR EXAMS. oh geez. i did okay i guess. we took them wednesday and tuesday, cuz jr's had a fieldtrip monday.
anyway, let's go over stuff..
steps for linearization:
1. Identify equation
2. Use f(x)+f ' (x)dx
3. Determine your dx
4. Then determine your x
5. Plug in everything
6. Solve
MEAN VALUE THEOREM:
If f is continous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a number c in (a,b) such that F'(c) = f(b) - f(a) / b-a\
EXTREME VALUE THEOREM:
the EVT states that a continuous function on a close interval [a,b], must have both a minimum and a maximum on the interval. However, the max and min can occur at the endpoints
steps for related rates:
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
normal lines & tangent lines & integrating trig functions! HELP NEEDED. go
For tangent lines, you are usually given an equation and a x-value.
ReplyDeleteAll you need to find from there, is a slope which you do by taking the derivative and plugging in the x-value and a y-value which is found by plugging the x-value into the original equation. Once you have a slope and a point, plug into point slope form ( y- y1)=m (x-x1).
Example: An equation to the line tangent to y= 4x^3 - 7x^2 at x=3 is
Find your y-value: 4(3)^3 - 7(3)^2 = 45
Now the slope: 12x^2 - 14x
12(3)^2 - 14(3) = 66
Plug into point slope: y-45 =66 (x-3)
Normal line is the same steps except you use the negative reciprocal of the slope instead
The normal line to the same equation at x=3 would be
y-45 = -1/66 ( x-3)
One way to integrate a trig functions is to sometimes to use your trig identities to simplify the original trig function
ReplyDeleteIntegrating Trig Functions:
ReplyDelete1. Opposite as derivatives..just memorize your Derivative formulas
2. Trig Identities that we learned in Advanced Math...remember and memorize them
3. Trig Identities that we learned in Calculus! Remember and memorize them...
See a pattern?
It's just a lot of memorizing really...=/