Grade 12 · Math · Calculus

12th grade The Mean Value Theorem worksheet

6 printable versionsChallenge Me10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

The Mean Value Theorem

Grade 12 Math Worksheet - Challenge Me

NameDate

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

f is differentiable, f(1) = 3, and f′(x) ≤ 5 for all x. Ari uses the Mean Value Theorem. What is the largest f(4) can be?
f is differentiable, f(0) = -1, and f′(x) ≤ 4 for all x. Bo uses the Mean Value Theorem. What is the largest f(6) can be?
f is differentiable, f(-1) = 7, and f′(x) ≤ 2 for all x. Jun uses the Mean Value Theorem. What is the largest f(4) can be?
Kira finds the c from the Mean Value Theorem for f(x) = √x on 1 ≤ x ≤ 9. What is c?
Luz finds the c from the Mean Value Theorem for f(x) = √x on 4 ≤ x ≤ 16. What is c?
Noah finds the c from the Mean Value Theorem for f(x) = √x on 9 ≤ x ≤ 25. What is c?
7.
f is differentiable on 1 ≤ x ≤ 5, with f(1) = 3 and f(5) = 11. Pia applies the Mean Value Theorem. Which must be true?
- some c between 1 and 5 has f′(c) = 8
- some c between 1 and 5 has f′(c) = 2
- f′(x) = 2 at each x between 1 and 5
- some c between 1 and 5 has f(c) = 2
8.
f is differentiable on 0 ≤ x ≤ 4, with f(0) = 10 and f(4) = -2. Ren applies the Mean Value Theorem. Which must be true?
- some c between 0 and 4 has f′(c) = -12
- some c between 0 and 4 has f′(c) = -3
- f′(x) = -3 at each x between 0 and 4
- some c between 0 and 4 has f(c) = -3
9.
f is differentiable on -2 ≤ x ≤ 4, with f(-2) = 5 and f(4) = 17. Tala applies the Mean Value Theorem. Which must be true?
- some c between -2 and 4 has f′(c) = 2
- some c between -2 and 4 has f′(c) = 12
- some c between -2 and 4 has f(c) = 2
- f′(x) = 2 at each x between -2 and 4
10.
f is differentiable on 2 ≤ x ≤ 6, with f(2) = 10 and f(6) = 30. Zee applies the Mean Value Theorem. Which must be true?
- some c between 2 and 6 has f(c) = 5
- f′(x) = 5 at each x between 2 and 6
- some c between 2 and 6 has f′(c) = 20
- some c between 2 and 6 has f′(c) = 5

12th grade The Mean Value Theorem worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

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

What your child will learn

I can find the average slope the theorem talks about.
I can find the c that the Mean Value Theorem or Rolle's theorem promises.
I can use the theorem to bound a value and say exactly what it guarantees.

Standard: none (beyond CCSS)

Words to know

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.

Common mistakes

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.

Questions parents ask

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.

More calculus

See all Calculus

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records