From f to f′ Problem set B Answers

1. (a) f′(x) = 2
2. (b) No: f′ is the horizontal line y = 2, which never meets the x-axis

1. (a) R
2. (b) x = −1

1. (a) P
2. (b) x = 0 and x = 2

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

1. (a) x = 0, x = 180 and x = 360
2. (b) \(180<x<360\)

g′(x) = 6x⁵

1. (a) J
2. (b) x = 4. The profit is at its greatest: it is neither rising nor falling there

An upward parabola meeting the x-axis at x = 0 and x = 2, below the axis for 0 < x < 2 and above it elsewhere.

f′ is zero at x = 90 and x = 270. It is positive for 0 ≤ x < 90 and 270 < x ≤ 360 and negative between, with its largest values at x = 0 and 360 and its smallest at x = 180: a cosine shape.