THIS WEEK IN CALC WE JUST WENT OVER ALL OF OUR A.P. STUFF, SAME AS THE REST OF THE THIRD 9 WEEKS, AND SAME THING WE WILL BE DOING FOR THE REST OF THE YEAR.
formulas for derivatives
d/dx c=0 (c is a #)
d/dx cu=cu' (c is #)
d/dx cx=c (c is a #)
d/dx u+v=u'+v'
d/dx uv=uv'+vu'
d/dx u/v=(vu'-uv')/v^2
d/dx sinx=cosx(x')
d/dx cosx=-sinx(x')
d/dx tanx=sec^2x(x')
d/dx secx=secxtanx(x')
d/dx cscx=-cscxtanx(x')
d/dx cotx=-csc^2x(x')
d/dx lnu= 1/u(u')
d/dx e^u=e^u(u')
***just remember that integration is opposite for all these derivative formulas. ***
Optimization can be used for finding the maximum/minimum amount of area of something. Steps in order to optimize anything:
1. Identify primary and secondary equations. Primary deals with the variable that is being maximized or minimized. The secondary equation is usually the other equation that ties in all the information given in the problem.
2. Solve the secondary equation for one variable and then plug that variable back into the primary. If the primary equation only have one variable you can skip this step.
3. Take the derivative of the primary equation after plugging in the variable, set it equal to zero, and then solve for the variable.
4. Plug that variable back into the secondary equation in order to solve for the last missing variable. Check endpoint if necessary to find the maximum or minimum answers
I'M NOT DOING SO GREAT ON AP RIGHT NOW, BUT HOPEFULLY ALL THE CORRECTIONS AND STUFF WILL HELP ME OUT. Can someone explain to me linearization. it has completely left my brain
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Ok, so for linearization, all you're doing is finding the equation for a tangent line.
ReplyDeleteSo say the question is as follows:
Approximate the value x=3.02 on the graph f(x) = x^3 +4x given the point (1,5).
So to find the slope, you're going to what? Take the derivative!
f'(x) = 3x^2 + 4
Then plug in the POINT that they gave you:
3(1)^2 + 4 = 7
Now, slope-intercept form using the point and the slope.
y - 5 = 7(x - 1)
Simplify:
y = 7x-2
Now you are just going to plug in what you're approximating!!!! which, in this case is 3.02!!!!
7(3.02) - 2
21.14-2
19.14====>SIMPLE AS THAT!!!!
linearization.
ReplyDeleteThe steps for solving linearization problems are:
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
to use linearization you first find your equation, then you figure out your dx after you figure out your x and last you plug everything in.
ReplyDelete