Grade 12 · Math · Calculus

12th grade The Mean Value Theorem worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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The Mean Value Theorem

Grade 12 Math Worksheet - Building Confidence

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Circle the best answer, or write your answer on the line.

For f(x) = x³ − 2x on 0 ≤ x ≤ 3, the Mean Value Theorem promises a c with f′(c) equal to one number. Ari finds that number. What is it?
For f(x) = x³ − 4x on 0 ≤ x ≤ 4, the Mean Value Theorem promises a c with f′(c) equal to one number. Esme finds that number. What is it?
For f(x) = x³ + 5x on -2 ≤ x ≤ 1, the Mean Value Theorem promises a c with f′(c) equal to one number. Jun finds that number. What is it?
Kira finds the c from the Mean Value Theorem for f(x) = x² + 3x on 2 ≤ x ≤ 6. What is c?
Luz finds the c from the Mean Value Theorem for f(x) = x² − 6x on 1 ≤ x ≤ 4. What is c?
Milo finds the c from the Mean Value Theorem for f(x) = x² + 5x on -1 ≤ x ≤ 4. What is c?
Pia finds the c from the Mean Value Theorem for f(x) = 8/x on 1 ≤ x ≤ 4. What is c?
Ren finds the c from the Mean Value Theorem for f(x) = 12/x on 2 ≤ x ≤ 8. What is c?
Tala finds the c from the Mean Value Theorem for f(x) = 9/x on 1 ≤ x ≤ 9. What is c?
Zee finds the c from the Mean Value Theorem for f(x) = 24/x on 4 ≤ x ≤ 9. What is c?

The Mean Value Theorem. Every version has 10 questions, and the answer key prints on the second page.

Standard: none (beyond CCSS)

Mean Value Theorem: Some c in (a, b) has f′(c) = (f(b) − f(a))/(b − a).

Rolle's theorem: If f(a) = f(b), some c has f′(c) = 0.

some c: At least one point, not every point.

Gave the change in f instead of the average slope. Divide by the length of the interval.

Subtracted earlier minus later, so the sign flipped.

Gave the slope instead of the point c where the derivative takes that slope.

What is the most common mistake with the mean value theorem?

Gave the change in f instead of the average slope. Divide by the length of the interval.

Are these 12th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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