Florida B.E.S.T. MA.912.C.3.1
The Standard
Find the slope of a curve at a point, including points at which there are vertical tangent lines.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the derivative and evaluate it at a given point to get the curve's slope. They use limits or graph behavior to recognize vertical tangents, where the slope is undefined.
What Mastery Looks Like
- Given a graph or equation, students correctly find a finite slope or identify a vertical tangent with undefined slope. They support the result using derivative values, limits, or tangent behavior.
Common Misconceptions
- Students may call a vertical tangent's slope zero or report infinity as a numerical slope. They may also assume every undefined derivative creates a vertical tangent, overlooking corners, cusps, and discontinuities.
How to Assess It
- Exit ticket: For y = x^(1/3), find the slope at x = 1, then use a limit to explain what happens at x = 0.
Lesson moves
Ways to Teach It
Trace printed curves with a ruler, rotate it to match the tangent at marked points, and record finite or vertical slopes.
Ask students to explain why a vertical tangent has undefined slope rather than zero slope.
Sort equation and graph cards into finite slope, vertical tangent, corner, cusp, and discontinuity groups.
Model a Ferris wheel with a circle, then locate positions where the cabin's path has horizontal or vertical tangent lines.
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Printable MA.912.C.3.1 Worksheet
A ready-to-print activity worksheet aligned to MA.912.C.3.1, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- MA.912.C.3.5
Determine the concavity and points of inflection of a function using its second derivative.
- MA.912.C.5.5
Find the area between a curve and the x-axis or between two curves by using definite integrals.
- MA.8.AR.3.2
Given a table, graph or written description of a linear relationship, determine the slope.
- MA.912.C.3.2
Find an equation for the tangent line to a curve at a point and use it to make local linear approximation.
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