From f′ to f Problem set A Answers

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

1. (a) \(-1<x<3\)
2. (b) x = −1 and x = 3

1. (a) \(2<x<5\)
2. (b) x = 5

1. (a) \(-1<x<2\) or \(x>4\)
2. (b) x = −1, x = 2, x = 4

1. (a) x = 5
2. (b) A maximum
3. (c) A straight line with gradient 3, increasing everywhere, with no stationary point

1. (a) 4
2. (b) f is increasing for all x > 0, but its gradient gets smaller: f keeps rising and flattens out

1. (a) \(0\le t<1\) or \(5<t\le 6\)
2. (b) t = 5

Stationary point at x = 4, a maximum. f rises up to x = 4 and falls after it: an upside-down U (like a downward parabola).

f is increasing for all x > 0 and passes through (1, 2). It is steep near x = 1 (gradient 6) and flattens as x grows (gradient 1 at x = 6). It has no stationary point.