Calculus I, Fall 2011 (http://www.math.nthu.edu.tw/˜ wangwc/)

Homework Assignment for Week 07

Assigned Oct 27, 2011.

1. Section 4.4: Problems 23, 29, 35, 41, 58 (Just graph it).

2. Section 4.5: Problems 3, 5, 13, 23, 25, 26, 27(a), 33, 36.

3. Section 4.6: Problems 13, 23(b), 25, 26, 28, 29, 33.

4. Read and compare the difference between Intermediate Value Theorem and Mean Value Theorem.

5. Suppose f is continuous on (−1, 1), differentiable on (−1, 0)∪(0, 1) and lim_{x→0}f′(x) exists. Show that f′(0) exists.

6. Suppose f is continuous on [a, b], differentiable on (a, b) and f(a) < f(b). Show that there are infinitely many x ∈ (a, b) such that f′(x) > 0.