50_Min_Distance.pdf

# 50_Min_Distance.pdf - Finding minimum distances Strategy to...

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Finding minimum distances Strategy to tackle the problem (1) Identify the variable to be minimized (here will be the distance D ), and assign symbols to other given quantities. (Give the variables names). (2) Identify the relation that allow us to write down an equality (referred as the primary equation) expressing D in terms of other quantities. (Usually such a rela- tionship can be found from facts in geometry). (3) Reduce the primary equation into one that express D in terms of a single inde- pendent variable. (This may involve the use of a secondary equation). Determine the domain. (Where can the independent variable take values from?) (4) Use calculus (derivative, critical numbers, comparison or appropriate discussions we learn from calculus). Example 1 Which points on the graph y = 4 - x 2 are closest to the point (0 , 2)? Solution: (1) Let D denote the distance from a point ( x, y ) on the graph to the on given point (0 , 2). (2) Express the distance in terms of x and y . From the distance formula, the primary equation is D = ( x - 0) 2 + ( y - 2) 2 . (3) We recognize that

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• Fall '10

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