this week in calc we did our first actual AP and got a score from 1-5. I got a 2, & was 11 points from passing. :( hopefully these next few weeks i can improve what i'm lacking in most, which is FREE RESPONSE. i got 0/27 then a 3/27.
OPTIMIZATION!:
1. Identify primary and secondary equations. Primary deals with the variable that is being maximized or minimized. The secondary equation is the other one.
2. Solve the secondary equation for one variable
3. Plug ^that variable back into the primary. If the primary equation only has one variable you can skip this step.
4. Take the derivative of the primary equation after plugging in the variable
5. Set it equal to zero and solve.
6. Plug that variable back into the secondary equation in order to solve for the last missing variable.
ABSOLUTE MAX/MIN!:
1. First derivative test
2. Plug critical values into the origonal function to get y-values
3. Plug endpoints into the origional function to get y-values
4. The highest y-value is the absolute maximum
5. The lowest y-value is the absolute minimum
since i did so horribly on free response, my question is going to be all of it. ha, i didn't know barely any of them! if someone wants to explain parts of it, or at least one problem. that would be very helpful
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6a on noncalc
ReplyDeletef(0) = 2 f'(0) = -4 f''(0) = 3
a. You are given g(x) = e^ax + f(x) for all real numbers where a is a constant and you are looking for g'(0) and g''(0) in terms of a.
To find g'(0), take the derivative of g.
g'(x) = a e^ax + f'(x)
and to find g'(0) plug in 0 for x
g'(0) = a e^a(0) + f'(0) = a (1) + -4 (look to what is given)
g'(0) = a -4
Next is asking for g''(0) so you will do the same thing
Take the derivative of g'(x) then plug in 0.
a e^ax a + f''(x)
g''(x) = a^2 e^ax + f''(x)
g''(0) = a^2 e^a(0) + f''(0)
g''(0) = a^2 (1) + 3
g''(0) = a^2 + 3
here it is:
ReplyDeleteon the 2006 Free Responce number 2...part A
it says to find the total number of cars turning left at the intersection over the time interval 0 less than or equal to t less than or equal to 18 hours, so you will integrate the formula given...
integrate from 0-18 of 60 squareroot of "t" times sin^2(t divided by 3).....you can plug that into your calculator and get 1658 cars.
here's the justification:
Knowing that I have to find a number from an equation and it has to be between something. I took the integral from 0 to 18 of the equation given and my answer became 1658.
HOPE THIS HELPS!
I'll explain area and volume problems because I'm decent at those. When you have a graph and it's asking for area follow these steps:
ReplyDelete1. find the bounds of the integral by plugging the graph into your calculator, 2nd calc, intersect to find the intersection points. These will be your bounds
2. Set the bounds to your integral (top-bottom)
3. Integrate
For volume:
1. Use the same bounds
2. pi (integral from bounds ((top)^2-(bottom)^2)
I'll try to help you on the area problems on the calculator portion. When they give you a graph and they want you to find the area, you plug in the two functions they give you in your calculator and graph them. To find the bounds you find the intersection between the two equations. The area formula is S (top)-(bottom). Then plug it into the FnT function on your calculator and solve. Hope this helps!
ReplyDeletewhat i've noticed on the free response is, there is almost always a reimann summ problem, and it's usually trapezoidal, so just know the formulas and you pretty much have at least one answer guaranteed to be correct
ReplyDelete