Mississippi Math C.A.10
The Standard
State and apply the formal definition of a derivative.
2025 Mississippi College- and Career-Readiness Standards for Mathematics · Use the Definition and Formal Rules of Differentiation to Compute Derivatives
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students state the derivative as the limit of a difference quotient. They use that limit to find a slope at one point or a slope formula for a function.
What Mastery Looks Like
- Given f(x)=x²+3x, a student expands f(x+h), cancels h, and gets f′(x)=2x+3. They can explain why h approaches zero but cannot be set to zero in the original fraction.
Common Misconceptions
- Some students expand (x+h)² as x²+h². Others set h=0 before canceling h, or mistake the slope between two points for the derivative at one point.
How to Assess It
- Exit ticket: State the limit definition of f′(x), then use it to find f′(x) for f(x)=x²+3x. Show the expansion and cancellation before taking the limit.
Lesson moves
Ways to Teach It
On graph paper, plot y=x² and draw secants from x=2 to x=3, 2.5, and 2.1; calculate each slope.
Ask partners to write why setting h=0 in ((2+h)²−4)/h fails and what they must do first.
Give pairs cards labeled x², x²+1, and 3x²; draw x=1 or x=2, then find the derivative there using the limit.
Use s(t)=t² meters for a moving cart; calculate its speed at t=3 seconds from the limit of average speeds.
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Printable C.A.10 Worksheet
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Related Standards
- C.A.14
Define a derivative and explain the purpose/utility of the derivative.
- C.A.15
Apply the derivative as a rate of change in varied contexts, including velocity, speed, and acceleration.
- C.A.20
State and apply the First and Second Fundamental Theorem of Calculus.
- C.A.17
Predict and explain the relationships between functions and their derivatives.
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