Linear approximation

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   The side of Esme's square tile changes from 10 cm to 10.15 cm. Use A′(s) = 2s to estimate the change in its area, in cm². What is it?

   3
2. 2.

   The side of Jun's square photo changes from 8 cm to 8.25 cm. Use A′(s) = 2s to estimate the change in its area, in cm². What is it?

   4
3. 3.

   The side of Kira's square garden plot changes from 15 cm to 15.2 cm. Use A′(s) = 2s to estimate the change in its area, in cm². What is it?

   6
4. 4.

   The side of Luz's square ice sheet changes from 12 cm to 11.9 cm. Use A′(s) = 2s to estimate the change in its area, in cm². What is it?

   -2.4
5. 5.

   Milo wants to estimate √50 with a tangent line. Which center a gives the best estimate?

   • a = 49, a perfect square close to 50
   • a = 36, a perfect square further below 50
   • a = 50, the number itself
6. 6.

   Noah wants to estimate ∛28 with a tangent line. Which center a gives the best estimate?

   • a = 28, the number itself
   • a = 8, a perfect cube further below 28
   • a = 27, a perfect cube close to 28
7. 7.

   Zee wants to estimate ∛63 with a tangent line. Which center a gives the best estimate?

   • a = 64, a perfect cube close to 63
   • a = 63, the number itself
   • a = 27, a perfect cube further below 63
8. 8.

   The linearization of Pia's function f at x = 2 is L(x) = −1 + 4(x − 2). What are f(2) and f′(2)?

   • f(2) = 4 and f′(2) = −1
   • f(2) = −1 and f′(2) = 4
   • f(2) = −1 and f′(2) = 2
9. 9.

   The linearization of Bo's function f at x = 6 is L(x) = 7 − 0.5(x − 6). What are f(6) and f′(6)?

   • f(6) = 7 and f′(6) = −0.5
   • f(6) = 7 and f′(6) = 6
   • f(6) = −0.5 and f′(6) = 7
10. 10.

    The linearization of Ari's function f at x = −1 is L(x) = 3 + 6(x + 1). What are f(−1) and f′(−1)?

    • f(−1) = 6 and f′(−1) = 3
    • f(−1) = 3 and f′(−1) = −1
    • f(−1) = 3 and f′(−1) = 6