Related Rate Applications Click here to skip to Optimization

In a nut shell: Relate rate problems typically involve word problems where you are
to find one or more rates (change of a function such as area, length, radius, height,
angle, etc , with respect to time.) The table below outlines a typical strategy.

Strategy:

1.	Draw a clear picture of the situation assigning names to each variable.
2.	Identify the unknown quantity of interest, “dependent quantity”.
3.	Express, in general terms, the unknown quantity in terms of the other variables.
4.	Take the derivative of the unknown quantity to obtain the desired rate.
5.	Substitute in specific values for the given conditions provided.
6.	Solve for the desired rate.

Example: Two cars are traveling towards an intersection. Car A is heading due south

at 50 mph and is 0.5 miles from the intersection. Car B is heading due west at 40 mph

and is 0.25 miles from the intersection. Find the rate of change of the distance between

the two cars at this instant.

Apply the Pythagorean theorem to unknown distance, D (hypoteneuse) in general terms.

D = √ ( x² + y² ) then use implicit differentiation

dD/dt = ½ ( x² + y² ) ^-1/2 [ 2x dxdt + 2y dy/dt ]

Put in given values: x = 0.25, y = 0.5, dy/dt = - 50, dx/dt = - 40

Then dD/dt = -62.6 mph Click here for two other examples.

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