whew... i got through the caluclus exam without to many headaches :), but by doing all of those study guides helped me to understand some problems that i didn't understand before.. one of those is tangent line.
1. take the derivative of the function... then plug the x value they give you into the derivative and get the slope.
2. If they do not give you a y value, you have to plug the x value into the original function to get it.
3. After you have all the variables, you can set the equation up into the form y-y1=slope(x-x1).
Another thing i'm feeling better about is surprisingly optimization...
1. First things first, finding the primary and secondary functions are a must, your primary function will always be what they are asking for such as (maximize area, perimeter, etc.)
2. Once you find those, use your primary function to solve for one variable.
3. Once you find that variable, you plug it into its designated spot in the secondary function, then simplify.
4. Once that is done, take the derivative, set it equal to zero and solve for the remaining variable. One variable will be solved for.
5. Once you find the remaining variable, you plug it back into the equation where you solved for the first variable. Your other variable will be solved for.
Now lets get into the stuff we learned on Friday: implicit derivatives
Basically, you find implicit derivatives the same way you find ordinary derivatives, the only difference is that implicit derivatives have two variables in them.
So you take the derivative as usual and when you take the derivative of a y, you must put dy/dx behind it, because that is what you will be solving for.
This is where i get stuck, i know how to take the derivative, but when it comes to simplifying the derivatives and solving for dy/dx i get confused..
for example on the homework: on problem # 5
i took the derivative and got 3x^2-(x) (dy/dx) + (1) (y) + 2y dy/dx=0
from here i am confused on how to simplify the derivative and how to solve for dy/dx.. if someone can explain this to me it would help me to understand implicits better, Thanks :)
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Solving for dy/dx is pretty simple.
ReplyDeleteSubtract any term that doesn't have that in it to the right side.
You should now have (in your example) 2 terms on the side with dy/dx in them.
Factor or take out a dy/dx out of both of them. Now divide both sides of the equation by what was left after you took out the dy/dx.
do the same thing as you are solving for x just treat dy/dx as if it were an x just as john said.
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