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BuiltWithNOF
Related Rates 
Steps

Mathematics & Statistic Tutor Perth - SPSS Help   

When I say read the question,
 I mean
 READ THE QUESTION!!!

STEP ONE


Use your pens to act out the movements of the variables, notice which distances increase, decrease and which stay the same.

 
if the quantity is staying the same then the rate of change is zero
if the quantity is decreasing then the rate of change is negative
if the quantity is increasing then the rate of change is positive

On paper draw a diagram.

STEP TWO

Look at the shape and think of any formulae or equations that are associated with the shape.
Look at the units in the question
 eg  ms-1   this will be a length changing
       m2s-1 this will be an area changing
       m3s-1 this will be a volume changing
 

STEP THREE

Differentiate with respect to time as we want the rate at which something is happening not just a length area or volume. 
Look at the variables or letters, unless it is a ‘t’, then we will always multiply by the amount d(letter)/dt if not we are treating the letter as if it were the letter t!
Really does ‘r’ look like ‘t’ ?

So what do we do? We use the rules of differentiation ie Trigonometric, Logarithm Chain ... but if it is not a ‘t’ then DON’T FORGET TO WE MUTIPLY BY d(letter)/dt
This is now the General Expression of how the variables are changing towards each other.
 

STEP FOUR

Now we need to gather all the information to find a specific rate of change at some particular value. 
We will substitute the given values into the General Expression though we may need to do some more calculations to find the value of other variables
 

STEP FIVE

Now answer the question so which rate of change did you want? 
Just remember is the quantity changing or not,
if the quantity is staying the same then the rate of change is zero
if the quantity is decreasing then the rate of change is negative
if the quantity is increasing then the rate of change is positive

Use your pens to act out the movements of the variables, notice which quantities increase, decrease and which stay the same. 

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