From f′ to f Problem set B Answers

1. (a) \(x>3\)
2. (b) \(x<3\)

1. (a) \(x<-2\) or \(x>2\)
2. (b) x = −2 and x = 2

1. (a) \(-3<x<-1\)
2. (b) x = −1

1. (a) \(x<-3\) or \(0<x<2\)
2. (b) x = −3, x = 0, x = 2

1. (a) x = 2
2. (b) A minimum
3. (c) A straight line with gradient −2, decreasing everywhere, with no stationary point

1. (a) 2
2. (b) f is increasing for all x > 0, but its gradient gets smaller: f keeps rising and flattens out

1. (a) \(0\le t<2\) or \(7<t\le 8\)
2. (b) t = 7

Stationary point at x = 3, a minimum. f falls to x = 3 and rises after it: a U shape (like an upward parabola).

f is increasing for all x > 0 and passes through (1, 3). It is steep near x = 1 (gradient 5) and flattens as x grows (gradient 1 at x = 5). It has no stationary point.