Calculus BC: Applications of the Derivative

Problems

Problem : Suppose Andrea decides to open a lemonade stand and her grandfather agrees to buy her all the supplies she needs. Now she has to decide what price she will charge for the lemonade. The more she charges per cup, the fewer cups people will buy. Andrea (who happens to be a mathematician) figures that the number of cups she will sell if she charges x cents per cup is approximately given by the function

 c(x) = 1000e -x/5

What should Andrea charge to maximize her profits? How much will she make?

Problem : Find the minimum value of f (x) = - 2x 3 +3x 2 + 12x - 1 in the interval [1, 4] .

Problem : Does the function g(x) = 3 - 2x attain a minimum value on the interval (1, 3) ?

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