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2.8 Related Rates of Change

(A) Related Rates of Change


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


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


Example 1 (Rate of change of y and x)
Two variables, and y are related by the equation   y=4x+3x . 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+3x=4x+3x1dydx=43x2=43x2dydt=dydx×dxdt2=(43x2)×dxdtwhen x=32=(4332)×dxdt2=113×dxdtdxdt=611 unit s1

(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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