Linear approximation
Grade 12 Math Worksheet
Circle the best answer, or write your answer on the line.
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?
Jun's sunflower is h(20) = 42 cm tall on day 20 and growing at h′(20) = 0.8 cm per day. What is your estimate of h(23) in cm?
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?
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?
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
Noah estimates x² at x = 4.1 with the tangent line at x = 4. Is the estimate too big or too small?
- It is an underestimate, because x² is concave up
- It is an overestimate, because x² is concave up
- It is exact, because the tangent line touches x² at x = 4
Ren estimates eˣ at x = 0.2 with the tangent line at x = 0. Is the estimate too big or too small?
- It is exact, because the tangent line touches eˣ at x = 0
- It is an overestimate, because eˣ is concave up
- It is an underestimate, because eˣ is concave up
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 underestimate, because ln x is concave down
- It is an overestimate, because ln x is concave down
- It is exact, because the tangent line touches ln x at x = 1
Tala uses the tangent line to f(x) = x³ at x = 2 to estimate (2.1)³. What is the estimate?
Bo uses the tangent line to f(x) = x⁴ at x = 2 to estimate (2.1)⁴. What is the estimate?