Learning objectives
Translate a described situation into an equation relating two or more quantities that change with time, drawing a labeled diagram and using geometric formulae or similar triangles where needed
Differentiate the relating equation implicitly with respect to time using the chain rule to link the rates of change of the quantities
Substitute known quantities and rates only after differentiating, solve for the unknown rate and report it with the correct units and sign
Solve standard related-rates problems, including expanding or shrinking circles and spheres, filling or draining conical tanks, sliding ladders, moving shadows and approaching objects
Interpret the answer in context, explaining what the sign means and whether the quantity is increasing or decreasing at that instant
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