The second derivative and concavity Problem set B Answers

1. (a) 18
2. (b) 6

1. (a) 40
2. (b) 4

1. (a) 0.00537
2. (b) 655

1. (a) −1
2. (b) 1.25

x < 3

1. (a) Decreasing, concave-up.
2. (b) Increasing; concave-up from B to C, then concave-down from C to D.
3. (c) Decreasing, concave-down.

1. (a) −3 cm per week²
2. (b) Negative: the rate at which the plant is growing is decreasing (concave-down).

1. (a) 2.96 mg per litre per hour²
2. (b) Concave-up: the concentration falls more slowly as time passes.

−1.41 < x < 1.41

\(y''=18 e^{3 x}\); it is positive for all x, so concave-up.