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December 4, 2012

December 4, 2012. AIM : How do we use implicit differentiation to solve related rates?. Do Now :. HW3.3 Pg. 154 # 13 – 23 odd . Related Rates.

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December 4, 2012

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  1. December 4, 2012 AIM: How do we use implicit differentiation to solve related rates? Do Now: HW3.3 Pg. 154 # 13 – 23 odd

  2. Related Rates • Word Problems that use derivatives to find out how fast something is changing. We will be talking about things that are increasing, decreasing, growing, shrinking, etc. all with respect to time. • Examples: • Find the rate the volume of a box is increasing with respect to time: • Find the rate the area of a circle is increasing with respect to time

  3. In related rates problems, the idea is to compute the rate of change of one quantity in terms of the rate of change of another quantity (which may be more easily measured). The procedure is to find an equation that relates the two quantities and then use the Chain Rule to differentiate both sides with respect to time.

  4. Example 1 The radius of a circular oil slick expands at a rate of 3 m/min. How fast is the area of the oil slick increasing when the radius is 20 m? Step 1: Draw a picture, if possible, and label variables Step 2: Find an equation that relates the variables (sometimes given) and differentiate with respect to time (implicit) Step 3: Plug in given information to solve for the unknown variable

  5. Example 2 Water pours into a fish tank at a rate of 3 ft3/min. How fast is the water level rising if the base of the tank is a rectangle of dimensions 2 x 3 ft? Note: If any of the variables are constant (do not increase/decrease/or change in any way), plug in their values before you differentiate.

  6. Example 3 - The Cone Water pours into a conical tank of height 10 ft and radius 4 ft at a rate of 10 ft3 /min. How fast is the water level rising when it is 5 feet high?

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