From f to f′ Problem set A Answers

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

1. (a) Q
2. (b) x = 1

1. (a) R
2. (b) x = −1 and x = 1

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

1. (a) x = 90 and x = 270
2. (b) \(90<x<270\)

f′(x) = 5x⁴

1. (a) R
2. (b) t = 2. The ball is at its highest point: it is neither rising nor falling for an instant

An upside-down parabola meeting the x-axis at x = −2 and x = 1, above the axis for −2 < x < 1 and below it elsewhere.

f′ is zero at x = 0, 180 and 360. It is negative for 0 < x < 180 and positive for 180 < x < 360, with its smallest value at x = 90 and its largest at x = 270: an upside-down sine shape.