12th grade Local and absolute extrema worksheet

Local and absolute extrema

Grade 12 Math Worksheet

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

1. 1.

   Ari finds the absolute maximum value of f(x) = x³ − 12x on −3 ≤ x ≤ 5. What is it?
2. 2.

   Bo finds the absolute maximum value of f(x) = x³ − 3x² on −1 ≤ x ≤ 4. What is it?
3. 3.

   Esme finds the absolute maximum value of f(x) = x³ − 27x on −4 ≤ x ≤ 2. What is it?
4. 4.

   Jun finds the absolute maximum value of f(x) = x³ − 6x² on −2 ≤ x ≤ 5. What is it?
5. 5.

   Kira uses the first derivative test on f(x) = xe^(−2x). At what x does f have its local maximum?
6. 6.

   Luz uses the first derivative test on f(x) = xe^(−3x). At what x does f have its local maximum?
7. 7.

   Noah uses the first derivative test on f(x) = xe^(−5x). At what x does f have its local maximum?
8. 8.

   f′(x) = (x − 1)²(x + 3). Ren makes a sign chart for f′. Which describes every critical point of f?

   • local max at x = −3; local min at x = 1
   • local max at x = −3; neither at x = 1
   • local min at x = −3; neither at x = 1
9. 9.

   f′(x) = x(x − 3)². Tala makes a sign chart for f′. Which describes every critical point of f?

   • local min at x = 0; neither at x = 3
   • local max at x = 0; local min at x = 3
   • local max at x = 0; neither at x = 3
10. 10.

    f′(x) = (x + 4)(x − 1)(x − 5)². Zee makes a sign chart for f′. Which describes every critical point of f?

    • local max at x = 1; local min at x = −4 and 5
    • local max at x = −4; local min at x = 1; neither at x = 5
    • local max at x = 1; local min at x = −4; neither at x = 5