9.8 Related Rates of Change

(A) Related Rates of Change


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


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


Example 1 (Rate of change of y and x)
Two variables, x and y are related by the equation   y=4x+ 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=4x+ 3 x =4x+3 x 1 dy dx =43 x 2 =4 3 x 2 dy dt = dy dx × dx dt 2=( 4 3 x 2 )× dx dt when x=3 2=( 4 3 3 2 )× dx dt 2= 11 3 × dx dt dx dt = 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