Maximum and minimum points on a domain Problem set B Answers

1. (a) local maximum (−3, 58); local minimum (3, −50)
2. (b) 158 (at x = 7)

1. (a) local maximum (0, 5); local minimum (1.41, −7)
2. (b) 47.2 (at x = 2.50)

b = −18, c = 85

1. (a) x = 0.199 or 2.06
2. (b) x = 1.39

(−2, 16), (0, 0), (2, 16)

(−1.36, −8.14)

1. (a) (2, −9)
2. (b) −25 (at x = −2)

1. (a) \(20\le f(x)\le 33.3\)
2. (b) \(f(x)\ge -27\)

1. (a) x = 2 and x = 6
2. (b) \(2<x<6\)
3. (c) local maximum (2, 39); local minimum (6, 7)

1. (a) \(\frac{dy}{dx}=0\) when \(x=-2\)
2. (b) 3 at x = -3; 3 at x = -1
3. (c) Neither: the gradient is positive on both sides, so it does not change sign

1. (a) 380 MW when t = 18
2. (b) 20 MW when t = 0

a = 1, b = −3

1. (a) t = 2 and t = 6
2. (b) \(2<t<6\)
3. (c) local maximum 8.2 thousand euros at t = 2; local minimum 5 thousand euros at t = 6

1. (a) (−1, −61), (2, 128), (4, 64)
2. (b) \(f(x)\ge -61\)

a = 4, b = 8