## Lecture Notes: Monday, October 5, 1998

Fifth Homework
Assignment - for discussion at recitations on Thursday October 8,
Tuesday October 13, and Thursday October 15.

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

- 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.
**Section 2 (Relative Maxima and Minima)**
- Definitions
- Relative Maximum
- Relative Minimum
- Critical Point

- FACT: If a differentiable function f(x) has a relative max
or min at x=a, then f'(a) = 0.
- Converse is false. Ex: f(x) = x^3 at x=0. Note sign of f'
on either side of this critical point.

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