## Lecture Notes: Friday, October 2, 1998

Fifth Homework Assignment - for discussion at recitations on Th Oct 8, T Oct 13, and Th Oct 15.

### Chapter 3

• Section 7 (Differentials)
• tangent line approximations

See Figure 3.18 in the text

section 3.7, problems # 20, 28

•

### Chapter 4 Section 1 (Increasing and Decreasing Functions)

•  Mean Value Theorem: If f is continuous on [a,b] and differentiable on (a,b), then
• f(b) - f(a) = f'(c)(b -a) for some c between a and b.

This result is not stated in the text, but it is very important.

• Applications of the Mean Value Theorem:
• f'(x) > 0 on an interval implies f(x) is increasing there
• f'(x) < 0 on an interval implies f(x) is decreasing there
• f'(x) = 0 on an interval implies f(x) is constant there
• if f(x) and g(x) have the same derivative on an interval, then f(x) and g(x) differ by a constant on that interval.
• this fills in the missing steps in our derivation of the speed and position of a particle moving in a straight line under constant acceleration.

• Section 4.1, problems # 16, 24, 48.

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