12th grade Linear approximation worksheet

Linear approximation

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?
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?
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?
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?
8. 8.

   Pia uses the tangent line to f(x) = x² at x = 3 to estimate (3.05)². What is the estimate?
9. 9.

   Bo uses the tangent line to f(x) = x⁴ at x = 2 to estimate (2.1)⁴. What is the estimate?
10. 10.

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