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Related_Rates_Handout_Notes_p1

# Related_Rates_Handout_Notes_p1 - Ex A pebble is dropped...

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Related Rates In the last section we learned to differentiate implicitly defined functions by using the Chain Rule. In this section we will use the Chain Rule to find the rates of change of two or more variables with dy dx dV dr respect to time, giving us expressions such as —, —, —. —. dt dt dt dt = 5x* -6x+2] Find'-— ^vhen;e = 4, given that — = 2 when* = 4. \£/ r C8 Steps to Use When Solving a Related Rates Word Problem 1. Draw a figure if possible. 2. Assign variables and restate the problem, listing your given information and what you are asked to find. Notice whether the given rates of change are positive or negative. 3. Find an equation that relates the variables. 4. Differentiate with respect to time. 5. Substitute the given information, and solve for the unknown derivative. Be sure to include units with your answer.
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Unformatted text preview: Ex. A pebble is dropped into a calm pond, causing ripples in the shape of concentric circles. The ^ radius of the outer ripple is increasing at a constant rat&of 1 ft/sec. When the radius Js_4 ft, y \ "findthe rate at which the area of the disturbed water is changing. Step 1: Draw a figure. <f L &j\ Step 2: Assign variables and restate the problem, listing your given information and what you are asked to find. Notice whether the given rates of change are positive or negative. Step 3: Find an equation that relates the variables. If necessary, find a relationship among the variables that lets you eliminate one variable. Step 4: Differentiate with respect to time. Step 5: Substitute the given information, and solve for the unknown derivative. Be sure to include units with your answer,...
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