Grade 12 · Math · Calculus

12th grade The Mean Value Theorem worksheet

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

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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The Mean Value Theorem

Grade 12 Math Worksheet

NameDate

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

Bo finds the c from the Mean Value Theorem for f(x) = x³ + 4x on 0 ≤ x ≤ 7. What is c, to the nearest hundredth?
Esme finds the c from the Mean Value Theorem for f(x) = x³ − 5x on 0 ≤ x ≤ 2. What is c, to the nearest hundredth?
Jun finds the c from the Mean Value Theorem for f(x) = x³ + 2x on 0 ≤ x ≤ 5. What is c, to the nearest hundredth?
A drone moves smoothly from 5 km along its route at t = 0 h to 101 km at t = 6 h. What speed, in km/h, must Luz see it reach at some moment?
A boat moves smoothly from 12 km along its route at t = 0 h to 51 km at t = 3 h. What speed, in km/h, must Milo see it reach at some moment?
A bus moves smoothly from 20 km along its route at t = 0 h to 140 km at t = 8 h. What speed, in km/h, must Noah see it reach at some moment?
f(x) = x² − 6x + 4 has f(1) = f(5). Pia finds the c in 1 < x < 5 that Rolle's theorem promises. What is c?
f(x) = x² − 8x + 1 has f(1) = f(7). Ren finds the c in 1 < x < 7 that Rolle's theorem promises. What is c?
f(x) = x² + 4x + 7 has f(-5) = f(1). Tala finds the c in -5 < x < 1 that Rolle's theorem promises. What is c?
f(x) = x² − 10x + 10 has f(4) = f(6). Zee finds the c in 4 < x < 6 that Rolle's theorem promises. 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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