Classifying stationary points and inflection Problem set A Answers

1. (a) x < 3
2. (b) x > −2

(1, 11) local maximum; (5, −21) local minimum

(−2, −13) local minimum; (0, 3) local maximum; (2, −13) local minimum

(1.78, 7.33) local maximum

(1.39, −1.55) local minimum

(2.5, −0.419) local maximum

k = −8

a = −3, b = 5

1. (a) \(y''=3 \left(3 x + 2\right) e^{3 x}\)
2. (b) 6

x = 5, maximum P = 25 thousand dollars

1. (a) \(S''=24 - 6 t\)
2. (b) t = 4
3. (c) 58 thousand copies per month

A curve above the x-axis that rises and flattens, like y = √x.

(−1, −1) local minimum; (0, 0) stationary point of inflection