Florida B.E.S.T. MA.912.C.3.4
The Standard
Find local and absolute maximum and minimum points of a function.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students locate possible high and low points by finding where the derivative is zero or undefined and by checking interval endpoints. They classify each candidate and compare function values when a greatest or least value is required.
What Mastery Looks Like
- Students find critical numbers, include endpoints when needed, and evaluate the function at each candidate. They use derivative signs or another valid test to classify each point and justify their choices.
Common Misconceptions
- Students often check only where the derivative equals zero and forget undefined derivative points or closed-interval endpoints. They may confuse a local extremum with the greatest or least value on the entire domain.
How to Assess It
- Give students f(x) = x³ − 3x on [−2, 2]. Ask them to list all candidates, classify local extrema, and identify the greatest and least function values.
Lesson moves
Ways to Teach It
Give pairs a printed curve, sticky dots, and tangent strips to mark candidates, then verify each point using derivative signs.
Ask students to explain why an endpoint can be an absolute extremum but cannot pass the usual two-sided local test.
Play an extrema sort game where teams classify cards showing derivative sign charts as local maximum, local minimum, neither, or inconclusive.
Model a profit function for ticket sales, then have students find and interpret the price that gives the greatest profit.
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Printable MA.912.C.3.4 Worksheet
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Related Standards
- MA.912.C.3.3
Determine where a function is decreasing and increasing using its derivative.
- MA.912.AR.4.3
Given a table, equation or written description of an absolute value function, graph that function and determine its key features.
- MA.912.C.1.5
Find limits at infinity.
- MA.912.C.1.3
Find limits of rational functions that are undefined at a point.
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