12th grade Local and absolute extrema worksheet

Local and absolute extrema

Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   f′ is positive just left of x = 3 and negative just right of it. Ari uses the first derivative test. Which describes f at x = 3?

   • a local maximum at x = 3
   • an absolute maximum at x = 3
   • no maximum or minimum at x = 3
   • a local minimum at x = 3
2. 2.

   f′ is negative just left of x = 5 and positive just right of it. Esme uses the first derivative test. Which describes f at x = 5?

   • an absolute minimum at x = 5
   • no maximum or minimum at x = 5
   • a local minimum at x = 5
   • a local maximum at x = 5
3. 3.

   f′ is positive just left of x = −1 and negative just right of it. Jun uses the first derivative test. Which describes f at x = −1?

   • no maximum or minimum at x = −1
   • an absolute maximum at x = −1
   • a local minimum at x = −1
   • a local maximum at x = −1
4. 4.

   Kira uses the first derivative test on f(x) = x³ − 3x² − 24x. What is the local maximum value of f?
5. 5.

   Luz uses the first derivative test on f(x) = x³ − 3x² − 45x. What is the local maximum value of f?
6. 6.

   Milo uses the first derivative test on f(x) = x³ − 9x² − 21x. What is the local maximum value of f?
7. 7.

   Noah uses the first derivative test on f(x) = x³ + 6x² − 36x. What is the local maximum value of f?
8. 8.

   Pia finds the absolute minimum value of f(x) = x² − 6x + 4 on 0 ≤ x ≤ 7. What is it?
9. 9.

   Tala finds the absolute minimum value of f(x) = x² − 8x + 10 on 1 ≤ x ≤ 6. What is it?
10. 10.

    Zee finds the absolute minimum value of f(x) = x² − 10x + 20 on 2 ≤ x ≤ 9. What is it?