There are various reasons why we would want to find the extreme (maximum and minimum values) of a function. Fermat's Theorem tells us we can find local extreme points by looking at critical points. This process is known as the Closed Interval Method.
There are various reasons why we would want to find the extreme (maximum and minimum values) of a function. Fermat's Theorem tells us we can find local extreme points by looking at critical points. This process is known as the Closed Interval Method.
Basic Calculus 11 - Derivatives and Differentiation RulesJuan Miguel Palero
It is a powerpoint presentation that discusses about the lesson or topic of Derivatives and Differentiation Rules. It also encompasses some formulas, definitions and examples regarding the said topic.
How to find the roots of Nonlinear Equations?
Newton-Raphson method is not the only way!
How about a system of nonlinear equations?
#WikiCourses
https://wikicourses.wikispaces.com/Topic+Roots+of+Nonlinear+Equations
Solve nonlinear equations using bracketing methods: Bisection and False Position
#WikiCourses
https://wikicourses.wikispaces.com/Topic+Roots+of+Nonlinear+Equations
Secant method is mathematical Root finding method. Most of techniques like this method but it is useful and time managing strategy.
So, refer this method its is useful for root finding.
The closed interval method tells us how to find the extreme values of a continuous function defined on a closed, bounded interval: we check the end points and the critical points.
Basic Calculus 11 - Derivatives and Differentiation RulesJuan Miguel Palero
It is a powerpoint presentation that discusses about the lesson or topic of Derivatives and Differentiation Rules. It also encompasses some formulas, definitions and examples regarding the said topic.
How to find the roots of Nonlinear Equations?
Newton-Raphson method is not the only way!
How about a system of nonlinear equations?
#WikiCourses
https://wikicourses.wikispaces.com/Topic+Roots+of+Nonlinear+Equations
Solve nonlinear equations using bracketing methods: Bisection and False Position
#WikiCourses
https://wikicourses.wikispaces.com/Topic+Roots+of+Nonlinear+Equations
Secant method is mathematical Root finding method. Most of techniques like this method but it is useful and time managing strategy.
So, refer this method its is useful for root finding.
The closed interval method tells us how to find the extreme values of a continuous function defined on a closed, bounded interval: we check the end points and the critical points.
There are various reasons why we would want to find the extreme (maximum and minimum values) of a function. Fermat's Theorem tells us we can find local extreme points by looking at critical points. This process is known as the Closed Interval Method.
Lesson 18: Maximum and Minimum Values (Section 041 slides)Matthew Leingang
There are various reasons why we would want to find the extreme (maximum and minimum values) of a function. Fermat's Theorem tells us we can find local extreme points by looking at critical points. This process is known as the Closed Interval Method.
15–Puzzle Problem is State-space search problems.
Branch and Bound Algorithm is used to Solve this Problem.
The application follows International Standard.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
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Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
2. Why is this important?
• An important application of differential calculus are
problems dealing with optimization.
Examples:
• What is the shape of a can that minimizes manufacturing
cost?
• What is the maximum acceleration of a space
shuttle?
• What is the radius of a contracted windpipe that
expels air most rapidly during a cough?
3. Definition: Absolute Maximum &
Minimum
Absolute Maximum (global maximum)
A function f has an absolute maximum at c if f(c) ≥ f(x)
for all x in D, where D is the domain of f. The number f(c)
is called the maximum value of f on D.
Absolute Minimum (global minimum)
A function f has an absolute minimum at c if f(c) ≤ f(x)
for all x in D and the number f(c) is called the minimum
value of f on D.
The maximum and minimum values of f are called the extreme
values of f.
4. Find the Maximum and
Minimum ?
Minimum value f(a)
Maximum value
f(d)
Absolute Minimum value
at f (x) = 0
No Maximum value
No Minimum value
No Maximum value
5. Definition: Local Maximum &
Minimum
Local Maximum (relative maximum)
A function f has a local maximum at c if f(c) ≥ f(
x) when x is near c. [This means that f(c) ≥ f
(x) for all x in some open interval containing c.]
Local Minimum (relative minimum)
Similarly, f has a local minimum at c if f(c) ≤ f(
x) when x is near c.
6. Definition: Critical numbers
Critical Numbers
• A critical number of a function f is a number c in the
domain of f such that either f`’(c) = 0 or f’(c)
does not exist.
• If f has a local maximum or minimum at c, then c is a
critical number of f.
7. Closed Interval Method
Finding the absolute maximum and minimum values of a
continuous function f on a closed interval a, b:
1. Find the values of f at the critical numbers of f in a, b
.
2. Find the values of f at the endpoints of the interval.
3. The largest of the values from Steps 1 and 2 is the
absolute maximum value; the smallest of these values
is the absolute minimum value.
8. Increasing & Decreasing
Test
Increasing
If f’(x) > 0 on an interval,
then f is increasing on that
interval.
Decreasing
If f’(x) < 0 on an
interval, then f is decreasing
on that interval.
9. The First Derivative Test
• Suppose that c is a critical number of
a continuous function f.
• If f’ changes from positive to
negative at c, then f has a local
maximum at c.
• If f’ changes from negative to
positive at c, then f has a local
minimum at c.
• If f’ does not change sign at c, then f
has no local maximum or minimum at
c.
• Example:
If f’ is positive on both sides of c or
negative on both sides
Direction Critical
Point
Direction
+ c -
- c +
- c -
+ c +
10. Definition: Concave up & Down
Concave Up
• If the graph of f lies above
all of its tangents on an
interval I, then it is called
concave upward on I.
Concave Down
• If the graph of f lies below
all of its tangents on I, it is
called concave downward
on I.
11. Concavity Test
• If f”(x) > 0 for all x in I,
then the graph of f is
concave upward on I.
• If f”(x) < 0 for all x in I,
then the graph of f is
concave downward on I.
12. Definition: Inflection Points
• A point P on a curve y = f(
x) is called an inflection
point if f is continuous
there and the curve
changes from
• concave upward to
concave down- ward
• concave downward to
concave upward
at P.
13. The Second Derivative Test
• Suppose f’’ is continuous near c.
• If f’(c) = 0 and f’’(c) > 0,then f has a local minimum
at c.
• If f’(c) = 0and f”(c) < 0,then f has a local maximum at c.
Example of Second Derivative Test
