Calculus I, Fall 2021 (Thomas’ Calculus Early Transcendentals 13ed), http://www.math.nthu.edu.tw/˜ wangwc/

Brief solutions to selected problems in homework week 09

1. Section 4.1, problem 77: f′(x) = \frac{2}{3}(x − 2)^{\frac{−1}{3}} f′(x) > 0 on x > 2, f′(x) < 0 on x < 2. f′(2) does not exist. So x = 2 is the only critical point. It may or may not be a local extreme without further information. Check the signs of f′(x) on x > 2 and x < 2. It follows that x = 2 is indeed a local min.

2. Section 4.2, problem 19:

Figure 1: Section 4.3, problem 19

3. Section 4.2, problem 65:

Figure 2: Section 4.2, problem 65

4. Section 4.3, problem 74:

Figure 3: Section 4.3, problem 74

5. Section 4.3, problem 77:

Figure 4: Section 4.3, problem 77 4