## 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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