Thomas’ Calculus Early Transcendentals 12ed

Study Guide for Chap 04

1. Classify possible locations of global minimum or maximum for a continuous function on a closed interval.

2. Read and study the difference between Intermediate Value Theorem and Mean Value Theorem.

3. Study the proofs of Rolle’s Theorem and Mean Value Theorem.

4. Study how to determine whether a critical point is a local minimum, local maximum, or neither using the first derivative test.

5. Review procedures for sketching a curve. Such as how to determine whether the curve is increasing/decreasing and concave up/down.

6. Review how to determine a indeterminate form using L’Hôpital’s Rule. Go through all examples in section 4.5.

7. Review standard procedure for applied optimization: determine relevant range of the unknown, find possible locations of maximum/minimum, and how to verify a candidate point is actually a maximum/minimum.

8. Understand how to derive Newton’s method. Study examples where Newton’s method does not converge or converge to a wrong solution.

9. Understand the meaning of Antiderivatives and how to find them in the simple cases.