Linear approximation

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   The temperature of Esme's tea is T(10) = 68 °C, changing at T′(10) = −1.5 °C per minute. What is your estimate of T(12) in °C?

   65
2. 2.

   Kira's fish tank holds V(5) = 150 liters after 5 minutes, filling at V′(5) = 12 liters per minute. What is your estimate of V(5.5) in liters?

   156
3. 3.

   Luz's balloon has radius r(30) = 9 cm at 30 seconds, growing at r′(30) = 0.4 cm per second. What is your estimate of r(26) in cm?

   7.4
4. 4.

   Milo estimates √x at x = 9.5 with the tangent line at x = 9. Is the estimate too big or too small?

   • It is an underestimate, because √x is concave down
   • It is exact, because the tangent line touches √x at x = 9
   • It is an overestimate, because √x is concave down
5. 5.

   Ren estimates eˣ at x = 0.2 with the tangent line at x = 0. Is the estimate too big or too small?

   • It is an underestimate, because eˣ is concave up
   • It is an overestimate, because eˣ is concave up
   • It is exact, because the tangent line touches eˣ at x = 0
6. 6.

   Zee estimates ln x at x = 1.3 with the tangent line at x = 1. Is the estimate too big or too small?

   • It is an overestimate, because ln x is concave down
   • It is an underestimate, because ln x is concave down
   • It is exact, because the tangent line touches ln x at x = 1
7. 7.

   Tala uses the tangent line to f(x) = x³ at x = 2 to estimate (2.1)³. What is the estimate?

   9.2
8. 8.

   Pia uses the tangent line to f(x) = x² at x = 3 to estimate (3.05)². What is the estimate?

   9.3
9. 9.

   Bo uses the tangent line to f(x) = x⁴ at x = 2 to estimate (2.1)⁴. What is the estimate?

   19.2
10. 10.

    Ari uses the tangent line to f(x) = x³ at x = 5 to estimate (4.9)³. What is the estimate?

    117.5