9.8 Related Rates of Change

(A) Related Rates of Change


1. If two variables xand y are connected by the equation y = f(x)


Notes:
If x changes at the rate of 5 cms -1 Þ  d x d t = 5
Decreases/leaks/reduces Þ  NEGATIVES values!!!


Example 1 (Rate of change of y and x)
Two variables, xand y are related by the equation   y = 4 x + 3 x . Given that y increases at a constant rate of 2 units per second, find the rate of change of x when x = 3.

Solution:
y = 4 x + 3 x = 4 x + 3 x 1 d y d x = 4 3 x 2 = 4 3 x 2 d y d t = d y d x × d x d t 2 = ( 4 3 x 2 ) × d x d t when  x = 3 2 = ( 4 3 3 2 ) × d x d t 2 = 11 3 × d x d t d x d t = 6 11  unit  s 1


(B) Rates of Change of Volume, Area, Radius, Height and 
      Length



(C) Rate of Change of Any Combination of Two Variables


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