The second derivative and concavity Problem set A Answers

1. (a) 14
2. (b) 8

1. (a) 46
2. (b) 22

1. (a) 0.0223
2. (b) 1090

1. (a) −1.5
2. (b) 0.75

x < 2

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

1. (a) 6 litres per minute²
2. (b) Positive: the rate at which the volume is increasing is increasing (concave-up).

1. (a) 536.26 dollars per year²
2. (b) Concave-up: the car loses value more slowly as it gets older.

−1.15 < x < 1.15

\(y''=4 e^{- x}\); it is positive for all x, so concave-up.