Maximum and minimum points on a domain Problem set A Answers

1. (a) local maximum (−2, 21); local minimum (2, −11)
2. (b) 70 (at x = 5)

1. (a) local maximum (0, 1); local minimum (−1.50, −9.13) and (1.50, −9.13)
2. (b) 82 (at x = 3)

b = −8, c = 11

1. (a) x = 0.342 or 1.38
2. (b) x = 0.942

(−2.45, 36), (0, 0), (2.45, 36)

(−1.39, −12.5)

1. (a) (1.86, −8.21)
2. (b) −36 (at x = −2)

1. (a) \(12\le f(x)\le 18.3\)
2. (b) \(f(x)\ge -19\)

1. (a) x = 1 and x = 5
2. (b) \(1<x<5\)
3. (c) local maximum (1, 11); local minimum (5, -21)

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

1. (a) 25.3 °C when t = 24
2. (b) 5.80 °C when t = 17.7

a = 2, b = −3

1. (a) t = 3 and t = 9
2. (b) \(3<t<9\)
3. (c) local maximum 30.8 m at t = 3; local minimum 20 m at t = 9

1. (a) (−2, −80), (2, 48), (3, 45)
2. (b) \(f(x)\ge -80\)

a = 0.5, b = 8