Florida B.E.S.T. MA.912.C.3.7
The Standard
Solve optimization problems using derivatives.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students define variables, turn constraints into an objective function in one variable, and state a reasonable domain. They use the derivative to find critical points and compare them with endpoints when needed. They interpret the best value in context.
What Mastery Looks Like
- A student can build an objective function from a written situation and reduce it to one variable. They find all valid candidates, including endpoints when needed, and justify the maximum or minimum. They give a labeled answer that fits the situation.
Common Misconceptions
- Students may optimize the constraint instead of the quantity named in the question. They may set the derivative equal to zero but ignore the valid domain and endpoints. They may report a variable value instead of the requested dimensions, area, volume, or cost.
How to Assess It
- Exit ticket: A farmer has 100 meters of fencing for three sides of a rectangle along a river. Find the dimensions that give the greatest area, and show how the derivative supports your answer.
Lesson moves
Ways to Teach It
Cut equal squares from the corners of cardstock, fold open boxes, measure volumes, then compare results with a derivative model.
Ask students to explain why a critical point is only a candidate and how endpoints can change the answer.
Run a card sort matching situation cards with variables, constraints, objective functions, valid domains, and final interpretations.
Plan a rectangular dog park against an existing wall using 80 meters of fencing, and find the dimensions with greatest area.
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