Calculus Ch 5 1 Critical Points Max Mins
- Slides: 19
Calculus Ch 5. 1 Critical Points, Max Mins
CRITICAL POINT f’(c) = 0 or f’(c) is undefined c is in the INTERIOR of the domain !!
To find max & mins for f(x), 1. Find f ' (x). 2. Factor. Set = 0 to find critical points.
3. Use a NUMBER LINE for a VISUAL. Examine points to the left and right of CRITICAL POINTS. Mark + and – signs to show where graph rises & falls.
a b c d f ’(a) is vertical = undefine It’s a critical point.
a b c d f ’(b) is horizontal = 0 Critical point
a b c d f ’(c) is sharp = undefine Critical point
a b c d f ’(d) is not in the interior. No critical point.
First derivative: Y’ is + graph increases. Y’ is neg graph decreases. Y’ = 0 Possible max or min.
1 st deriv Find critical poin If f is negative to the left o and + to the right of c, you have a local min. f falls f rises + c
1 st deriv Find critical poin If f is + to the left of c and negative to the right of c, y have a local MIN. f rises f falls+ c
Determine max and mins Extreme Value Th: If f is continuous on [a, b], f has a global max and min on [a Also known as absolute
Extreme Value Th: global max at c on [a, b] if f(x) < f(c) for all x. global min at c on [a, b] if f(x) > f(c) for all x.
Graph Roots are x= -1 and x= 2 x intercepts -1 2
First Deriv test 0 2
neg + + 0 2
Possible max a min at 2. - graph + + graph falls rises 0 2
y= 2 (x+1)(x-2) roots -1, 2 nd 2 deriv tells about concavity -1 0
If c is a Critical number of f has a local minimum at if f(c) < f(x) for all x near c If c is a Critical number o f has a local maximum at if f(c) > f(x) for all x near c
- Calculus critical points
- Principle of sterilization
- Critical semi critical and non critical instruments
- Www.mathsrevision.com
- 1*60
- 65 mins
- Local max
- Mass media
- Brand positioning bull's eye
- Points of parity and points of difference
- Objectives of haccp
- Types of critical points
- Relative extreme values
- Quadratic inequality examples
- Haccp training materials
- Critical decision points
- Examples of critical control points
- Critical reading meaning
- Calculus bridge
- Uva math placement test