Application Word Problem Continuity and Derivatives
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It costs Sugarco 25 cents/lb to purchase the first 100 lb of sugar 20 cents/lb to purchase the next 100 lb and 15 cents to buy each additional pound. Let f(x) be the cost of purchasing x pounds of sugar. Is f(x) continuous at all points? Are there any points where f(x) has no derivative?
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Solution Summary
Continuity and derivatives are investigated. The solution is detailed.
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We can define f(x) piece-wisely.
When 0<=x<=100, it costs 25 cents per pound, then f(x)=25x cents;
when 100<x<=200, the first 100 pounds costs 25*100=2500 cents and the additional x-100 pounds cost 20 cents for each ...
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