Local and absolute extrema

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   Ari finds the absolute maximum value of f(x) = x − 2 sin x on 0 ≤ x ≤ 2π. What is it, to the nearest hundredth?

   6.97
2. 2.

   Bo finds the absolute maximum value of f(x) = 2 sin x − x on π/6 ≤ x ≤ π. What is it, to the nearest hundredth?

   0.68
3. 3.

   Esme finds the absolute maximum value of f(x) = x + cos x on 0 ≤ x ≤ 2π. What is it, to the nearest hundredth?

   7.28
4. 4.

   Jun finds the absolute maximum value of f(x) = x − cos x on 0 ≤ x ≤ 2π. What is it, to the nearest hundredth?

   5.28
5. 5.

   Kira finds the smallest value of f(x) = x⁴ − 8x² + 10 over all real x. What is it?

   -6
6. 6.

   Milo finds the smallest value of f(x) = x⁴ − 50x² + 100 over all real x. What is it?

   -525
7. 7.

   Pia wants the absolute extrema of f(x) = x³ − 3x on 0 ≤ x ≤ 2. Which values must be compared?

   • f(0) and f(2)
   • f(−1), f(0), f(1) and f(2)
   • f(1) alone
   • f(0), f(1) and f(2)
8. 8.

   Ren wants the absolute extrema of f(x) = x³ − 12x on −3 ≤ x ≤ 1. Which values must be compared?

   • f(−3), f(−2), f(1) and f(2)
   • f(−3), f(−2) and f(1)
   • f(−3) and f(1)
   • f(−2) alone
9. 9.

   Tala wants the absolute extrema of f(x) = x³ − 27x on −1 ≤ x ≤ 4. Which values must be compared?

   • f(3) alone
   • f(−1) and f(4)
   • f(−3), f(−1), f(3) and f(4)
   • f(−1), f(3) and f(4)
10. 10.

    Zee wants the absolute extrema of f(x) = x⁴ − 8x² on −1 ≤ x ≤ 3. Which values must be compared?

    • f(−1), f(0), f(2) and f(3)
    • f(0) and f(2)
    • f(−2), f(−1), f(0), f(2) and f(3)
    • f(−1) and f(3)