This week in Calculus we took AP tests and then corrected them and did the key words packet. Suprisingly, i did semi-well on the AP tests..so i'm going to do the same thing I did last week in case it's good luck.
I'LL JUST REVIEW :)
So, lets start off with implicits.
They are really simple, but came up alot on the last two APs.
So, you know its implicit if you have x's and y's in the equation.
Everytime you take the derivative of y, you must put dy/dx.
So, problem time.
xy + 2x = 10
x(dy/dx) + y(1) = 0
Now, you simplify for dy/dx.
x(dy/dx) = -y
dy/dx = -y/x
As long as you remember your simple algebra rules and things about derivatives..these are really easy.
Next thing I'll explain is...tangent lines.
well half-way.
I know you take the derivative..then plug something in..
then take another derivative..or maybe plug in another number?
That's where i get confused..but i think it's mostly because i forgot how to do it.
and if they ask for a tangent line, and a line parallel to the tangent line
it should be the same thing, right?
Can anyone help me with that..
and a brush up on related rates and optimization.
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For related rates it is best to write out the given or to draw a picture. You then figure out what equation they are asking you to use if they do not give you one. Sometimes, you may have to use the Pythagorean theorem to find a leg or the rate of a leg if you are dealing with triangles. Next you plug in and take the derivative of the function and solve. Hope this helps!
ReplyDeleteokay so my computer was down last night so hopefully this will count cause i couldnt get on:
ReplyDeleteThe steps for related rates are:
1. Identify all of the variables and equations
2. Identify the things that you are looking for
3. Sketch a graph and then label that graph
4. Create and write an equation using all of the variables
5. Take the derivative of this equation with respect to time
6. Substitute everything back in
7. Solve the equation