The steps for related rates are:
1. Identify all your variables and equations. Some may be given, but some you may have to find.
2. Identify what you need to solve for.
3. Make a sketch or draw a picture of what you are given.
4. Take the derivative of the equations with respect to time.
5. Plug in given numbers to the derivative and solve.
EXAMPLE 1: The problem can be given as just and equation with given information such as :
x^2+y^2=25 dy/dt when x=3, y=4 dx/dt= 8
Derivative: 2x dx/dt + 2y dy/dt= 0
When you plug in you get: 2(3)(8) + 2(4) (dy/dt) = 0
48+ 8 dy/dt=0
dy/dt= -6
EXAMPLE 2: You may have to find the equation yourself:
The radius r of a circle is increasing at a rate of 3 centimeters per minute. Find the rates of change of the area when r=6 centimeters and when r=24 centimeters.
The area of a circle is A=pir^2
You are given dr/dt=3
Take the derivative of the equation: dA/dt=2pir (dr/dt)
Now plug into your derivative: dA/dt= 2pi(6)(3)
dA/dt= 36pi cm^2/min.
Using the same derivative, you plug in 24 into the equation instead of 6
dA/dt= 2 pi (24)(3)
dA/dt= 144 pi cm^2/min.
I understand the simple related rates problems such as these two; however, I don't understand how to work them when they get harder and give real life situations. The same thing applies for angle of elevation. I let the words get in the way and cannot find what they are asking for or what is given.
Help would be appreciated =)
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