wellll, for some reason, last week just seemed like a waste of a week because I wasn't really there, except for in calc because nothings ever a waste in there righttttt? right. anyways we went over the two AP exams we took the week before and identified key words which i think is going to help alot once it sinks in.
Example and explination of tangent lines:
1. Identify the equation and tangent poing. Plug the x value into the original equation if they don't already give you a y value.
2. Differentiate your equation.
3. Plug in x value then solve for dy/dx.
4. dy/dx value=slope, plug in to point slop form.
Find the line tangent to the graph y=2x2+4x+6 at x=1.
y=2x2+4x+6 y=2(1)2
dy/dx=4x+4
dy/dx=4(1)+4=8
(y-12)=8(x-1)
Slop fields are probably the easiest thing i've ever seen in my life.
* plug in the point on the graphy which are already given to you intooo the equation that is also already given and your answers depend on what what your outcome is and lines you draw for them.
The line for postitive slopes is /
The line for negative slope is \
The line for a zero slope is a horizontal line --
The line for an undefined slope is a vertical line
QUESTIONS: i've pretty much forgotten everything about related rates... help? pleaseeeeee?
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For related rates the first thing you should do is figure out what is given. We had a problem the other day on the non-calculator portion of the exam that dealt with related rates and a triangle. They gave you the hypotenuse, which is 5 ft. They have you one leg which is x equals 3. They also gave you the rate at which that leg is decreasing which is dx/dt which is 2. So we are solving for Da/dt, which is the rate the area is changing.
ReplyDeleteSo we know:
x=3
y=4
dx/dt=2
we don't know:
dy/dt
Da/dt
to find dy/dt, you plug in your given into the pythagorean theorum. so you get 5^2=x^2 +y^2, which gives you 25=x^2+y^2. Do solve for dy/dt you have to ge y by itself, so you get y^2= 25-x^2. Now take the derivative, 2y dy/dt= -2dx/dt. Now plug in what we know: 2(4)dy/dt=2(3)(-2). After solving that gives you dy/dt= 3/2.
We are not done yet lol. To solve for Da/dt, use the area of a triangle formula which is A=1/2xy. So take the derivative, Da/dt=1/2 dx/dt(y)+ dy/dt(x). Now plug in what you know, Da/dt= 1/2(-2)(4)+(3/2)(3). Da/dt equals = -7/4.. hope this helps.