2.6: Related Rates Olympic National Park, Washington.

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2.6: Related Rates Olympic National Park, Washington

2.6: Related Rates Olympic National Park, Washington

2.6: Related Rates Olympic National Park, Washington

As we already know variables are related through equations. For example, x and y can be related by y = 2x. If the variables are changing with respect to time, then their rates are also related by an equation. If y = 2x then: dy/dt = 2dx/dt If then: Basically, any rate of change with respect to time can be expressed as a derivative.

(Possible if the sphere is a soap bubble or a balloon.) Suppose that the radius of a sphere is increasing at a rate of 0.1 cm/sec. This is considered dr/dt. (Possible if the sphere is a soap bubble or a balloon.) Find how fast the volume is changing when the radius is 10 cm. The sphere is growing at a rate of .

Process for Related Rates Problems: 1. Draw a picture (sketch). 2. Write down known information. 3. Write down what you are looking for. 4. Write an equation to relate the variables. 5. Differentiate both sides with respect to t. 6. Evaluate.