Local and absolute extrema

Answer Key - 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 = −2 and positive just right of it. Bo uses the first derivative test. Which describes f at x = −2?

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

   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
   • a local maximum at x = 5
   • a local minimum at x = 5
   • no maximum or minimum at x = 5
4. 4.

   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?

   • a local minimum at x = −1
   • no maximum or minimum at x = −1
   • an absolute maximum at x = −1
   • a local maximum at x = −1
5. 5.

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

   81
6. 6.

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

   11
7. 7.

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

   216
8. 8.

   Ren finds the absolute minimum value of f(x) = x² + 2x + 5 on −3 ≤ x ≤ 2. What is it?

   4
9. 9.

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

   -6
10. 10.

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

    -5