Section You should be able to... Examples Review Exercises
4.1 1 Solve related rate problems (p. 255) 1–5 1–3
4.2 1 Identify absolute maximum and minimum values and local extreme values of a function (p. 263) 1 4, 5
2 Find critical numbers (p. 267) 2 6(a), 7
3 Find absolute maximum and absolute minimum values (p. 268) 3–6 8, 9
4.3 1 Use Rolle’s Theorem (p. 275) 1 10
2 Work with the Mean Value Theorem (p. 275) 2, 3 11, 12, 28
3 Identify where a function is increasing and decreasing (p. 279) 4–6 23(a), 24(a)
4.4 1 Use the First Derivative Test to find local extrema (p. 284) 1, 2 6(b), 13(a)–15(a)
2 Use the First Derivative Test with rectilinear motion (p. 286) 3 16
3 Determine the concavity of a function (p. 287) 4, 5 23(b), 24(b)
4 Find inflection points (p. 290) 6 23(c), 24(c)
5 Use the Second Derivative Test to find local extrema (p. 291) 7–8 13(b)–15(b)
4.5 1 Identify indeterminate forms of the type \(\dfrac{0}{0}\) and \(\dfrac{\infty }{\infty }\) (p. 298) 1 41–44
2 Use L'Hôpital's Rule to find a limit (p. 299) 2–6 45, 47, 49–52, 55
3 Find the limit of an indeterminate form of the type \(0\cdot \infty,\) & \(\infty -\infty\), \(0^{0}\), \(1^{\infty }\), or \(\infty ^{0}\) (p. 303) 7–10 46, 48, 53, 54, 56
4.6 1 Graph a function using calculus (p. 308) 1–7 17–22, 25, 26, 27
4.7 1 Solve optimization problems (p. 318) 1–6 29, 30, 61–63
4.8 1 Find antiderivatives (p. 329) 1, 2 31–38
2 Solve a differential equation (p. 331) 3, 4 57–60
3 Solve applied problems modeled by differential equations (p. 333) 5–7 39, 40, 64