AP Calculus AB

1
AP Calculus AB

• Day 1
• Section 3.1

2
Extreme Value Theorem
If f is continuous on a,b then f must have both
an absolute maximum and absolute minimum value in
the interval.
Examples
Absolute Maximum
Abs Max
Abs Max
Abs Min
Abs Min
Absolute Minimum
3
Extrema highest and lowest function values

• 3 types
• Absolute (See previous slide)
• Relative -- occur only at critical numbers
• (cannot be at endpoints of an interval)
• Local -- compared to the points around it
• (can be at endpoints and critical numbers)

when the derivative is either zero or undefined
Horizontal tangents
Vertical tangents
A/R/L
A/L
A/L
Local
R/L
Local
A/L
Local
R/L
A/R/L
A/R/L
Extrema will only occur at endpoints or critical
numbers!
4

• Find the extrema of
  on -1,3.

Extrema occur at either endpoints or critical
numbers.
f(x) is continuous on -1,3.
Minimum
Maximum
Vertical tangents
Horizontal tangents
5
AP Calculus AB

• Day 1
• Section 3.1

6
Extreme Value Theorem
If f is continuous on a,b then f must have both
an absolute maximum and absolute minimum value in
the interval.
Examples
7
Extrema

• 3 types
• Absolute
• Relative
• Local

8

• Find the extrema of
  on -1,3.