Mississippi Math C.A.16

MathGrades 9–12Algebra (A) Demonstrate Basic Knowledge of Functions, Including their Behavior and Characteristics

The Standard

Apply the derivative to find tangent lines and normal lines to given curves at given points.

2025 Mississippi College- and Career-Readiness Standards for Mathematics · Apply Derivatives to Find Solutions in a Variety of Situations

Teacher's field guide

What Students Need to Do: Students find the derivative and evaluate it at the given x-value to get the tangent slope. They use that slope and the given point to write the tangent line, then write the perpendicular normal line.
What Mastery Looks Like: For y=x² at (2,4), students find a tangent slope of 4 and a normal slope of -1/4. They write both line equations through (2,4). They know a horizontal tangent has a vertical normal.
Common Misconceptions: Students may treat the derivative as the tangent line equation rather than its slope. They may change the slope's sign but forget to take its reciprocal for the normal. A horizontal tangent can also trip them up because its normal is vertical.
How to Assess It: Exit ticket: For y=x² at (2,4), find the tangent and normal line equations. Show how you found each slope.

Lesson moves

Print a graph of y=x², then have students place rulers at (1,1) to draw the tangent and its perpendicular normal.
Ask students to explain why the tangent to y=x² at (0,0) is horizontal and the normal is vertical.
Give pairs cards showing curves, points, slopes, and line equations to match, using y=x² at (2,4) and y=x³ at (1,1).
Sketch a ramp with height y=0.1x², then find the ramp's tangent and a perpendicular brace at x=2.

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