Linear approximation

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Jun knows f(4) = 7 and f′(4) = −2. Use the tangent line at x = 4 to estimate f(4.3). What is the estimate?

   6.4
2. 2.

   Kira knows f(8) = 20 and f′(8) = 1.5. Use the tangent line at x = 8 to estimate f(8.4). What is the estimate?

   20.6
3. 3.

   Luz knows f(1) = −6 and f′(1) = 3. Use the tangent line at x = 1 to estimate f(0.9). What is the estimate?

   -6.3
4. 4.

   Milo wants the linearization of f(x) = √x at x = 9. Which is L(x)?

   • L(x) = 3 + (1/6)(x − 9)
   • L(x) = 9 + (1/6)(x − 3)
   • L(x) = 3 + (1/6)x
5. 5.

   Noah wants the linearization of f(x) = x³ at x = 2. Which is L(x)?

   • L(x) = 8 + 12(x − 2)
   • L(x) = 8 + 12x
   • L(x) = 2 + 12(x − 8)
6. 6.

   Ren wants the linearization of f(x) = 1/x at x = 2. Which is L(x)?

   • L(x) = 2 − (1/4)(x − 1/2)
   • L(x) = 1/2 − (1/4)x
   • L(x) = 1/2 − (1/4)(x − 2)
7. 7.

   Zee wants the linearization of f(x) = x² at x = 5. Which is L(x)?

   • L(x) = 25 + 10x
   • L(x) = 25 + 10(x − 5)
   • L(x) = 5 + 10(x − 25)
8. 8.

   Tala uses the tangent line to y = √x at x = 25 to estimate √26. What is the estimate?

   5.1
9. 9.

   Pia uses the tangent line to y = √x at x = 16 to estimate √17. What is the estimate?

   4.125
10. 10.

    Ari uses the tangent line to y = √x at x = 100 to estimate √104. What is the estimate?

    10.2