Calculus and Above

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The owner of a horse-boarding...

The owner of a horse-boarding stable wants to build exercise runs for three of her horses. She plans to fence off an 882 square meter rectangular area and divide it into three equal parts with two fences parallel to one of the sides.

(a) What dimensions for the outside rectangle will require the smallest total length of fence? (Show clearly how you used calculus to solve this problem).

(b) Students often describe their method for solving optimization problems as "set the derivative equal to zero and solve for x." Is the solution to an optimization problem always a point where the derivative is zero? If so, explain why. If not, explain why not.

(a) What dimensions for the outside rectangle will require the smallest total length of fence? (Show clearly how you used calculus to solve this problem).

(b) Students often describe their method for solving optimization problems as "set the derivative equal to zero and solve for x." Is the solution to an optimization problem always a point where the derivative is zero? If so, explain why. If not, explain why not.

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