Average and instantaneous rates of change

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   Ari finds that f(x) = x² has average rate of change 7 from x = 1 to x = b. What is b?

   6
2. 2.

   Bo finds that f(x) = x² has average rate of change 11 from x = 2 to x = b. What is b?

   9
3. 3.

   Esme finds that f(x) = x² has average rate of change 4 from x = -1 to x = b. What is b?

   5
4. 4.

   A ball thrown down falls s(t) = 4.9t² + 3t m after t seconds. Kira shrinks [2, 2 + h] to find the velocity at t = 2. What is it, in m/s?

   22.6
5. 5.

   A cart's position is s(t) = 3t² + 2t m after t seconds. Luz shrinks [3, 3 + h] to find the velocity at t = 3. What is it, in m/s?

   20
6. 6.

   A skater's position is s(t) = 0.5t² + 4t m after t seconds. Milo shrinks [4, 4 + h] to find the velocity at t = 4. What is it, in m/s?

   8
7. 7.

   A sled's position is s(t) = 2t² − 2t m after t seconds. Noah shrinks [5, 5 + h] to find the velocity at t = 5. What is it, in m/s?

   18
8. 8.

   Pia studies f(x) = 12/x. What is its average rate of change from x = 2 to x = 6?

   -1
9. 9.

   Ren studies f(x) = 6/x. What is its average rate of change from x = 1 to x = 3?

   -2
10. 10.

    Zee studies f(x) = 8/x. What is its average rate of change from x = 2 to x = 4?

    -1