This week we learned related rates and angle of elevation along with the implicit first and second derivatives. Implicit derivatives isn't too bad, i wasn't there for the notes but i still understand what i'm doing.
RELATED RATES: the problem can be given as a picture or they can tell you certain things which require you to draw the picture out yourself. Equations are sometimes provided and remember that you can only have one variable that you don't know what it is.
1. Identify all of the variables and equations.
2. Identify what you want to find.
3. Sketch and label.
4. Write an equations involving your variables.
5. Take the derivative with in terms of time.
6. Substitute the derivative in and solve.
IMPLICIT DERIVATIVES
1. take the derivative of both sides
2. everytime you take the derivative of y note it with dy/dx or y^1
3. solve for dy/dx
EXAMPLE: y^6+y^4-10y-x^4=-8
6y^5dy/dx+4y^3dy/dx-10dy/dx-4x^3+0
dy/dx(6y^5+4y^3-10)=4x^3
dy/dx=4x^3/6y^5+4y^3-10
once again, i get the whole derivatives concept, however, i have no idea what i'm doing with related rates. i can draw the picture, but thats about it. i have a hard time applying outside things or relating thing that aren't given to the problem. any help would be great, thankssssssss.
write down your given like we do in physics...make sure to draw a picture! we get points for that i think...then find the missing angle cause we have to use it in the equation tan(theta)=opp/adj. After you solve, take the derivative. and now, whatever that gives you, you plug into the original forumla [hopefully they give you that in the problem]. Then once everything is solved for that's your answer!....hope this helps!
ReplyDelete1. Identify all variables and equations
ReplyDelete2. Identify what you are looking for
3. Make a sketch and label
4. Write an equation involving your variables
5. Take the derivative with respect to time
6. Substitute in derivative and solve.
Basically, identify what's given and what you're looking for. Draw a picture. Make an equation (usually area, volume, pythagorean theorm). Take the derivative. Plug in and solve ^^
ReplyDelete