Western Normal University Edition First Grade Mathematics Volume 1
Beijing Normal University Edition Seventh Grade Mathematics Volume 1
People's Education Press First Grade Mathematics Volume 1
People's Education Press Second Grade Mathematics Volume 1
People's Education Press Third Grade Mathematics Volume 1
Beijing Normal University Edition Seventh Grade Mathematics Volume 2
Qingdao Edition Seventh Grade Mathematics Volume 1
Beijing Normal University Edition Fifth Grade Mathematics Volume 1
Hebei Education Edition Third Grade Mathematics Volume 1
Beijing Normal University Edition Eighth Grade Mathematics Volume 1
People's Education High School Mathematics Edition B Compulsory Course 2
Hebei Education Edition Seventh Grade Mathematics Volume 2
Hebei Education Edition Fourth Grade Mathematics Volume 2
Beijing Normal University Edition Fifth Grade Mathematics Volume 2
Qingdao Edition Seventh Grade Mathematics Volume 2
People's Education Press First Grade Mathematics Volume 2
Category | Format | Size |
---|---|---|
People's Education High School Mathematics Edition A Compulsory Course 1 | pptx | 6 MB |
Description
"Basic Inequalities" Quadratic functions, equations and inequalities PPT
Part One: Explanation of Curriculum Standards
1. Understand the basic inequality √ab≤(a+b)/2(a,b≥0).
2. Be able to use basic inequalities to solve simple maximum or minimum problems.
3. Be able to use basic inequalities to prove inequalities and compare the magnitude of algebraic expressions.
Basic Inequalities PPT, Part 2: Independent Learning
1. Basic Inequalities
1. (1) In the last lesson, we learned an important inequality: if a, b∈R, then a2+b2≥2ab (the equal sign holds true if and only if a=b). If a>0 ,b>0, we replace a and b in the inequality with √a and √b respectively. What form can we get?
Hint: get a+b≥2√ab.
(2) We often write this inequality as √ab≤(a+b)/2(a>0,b>0), and call this inequality "basic inequality". What are the conditions for the equality sign to hold?
Tip: The equal sign holds true if and only if a=b.
(3) We call √ab the geometric mean of a and b, and (a+b)/2 the arithmetic mean of a and b. How to use these two concepts to describe basic inequalities?
Tip: The basic inequality can be stated as: the arithmetic mean of two positive numbers is not less than their geometric mean.
(4) As shown in the figure, AB is the diameter of the circle, point C is a point on AB, AC=a, BC=b. Draw a chord DD' perpendicular to AB through point C, connecting AD and BD.
2. Use basic inequalities to find the optimal value
1. Fill out the two forms below:
Based on the above table and combined with basic inequality analysis:
(1) When x+y is a constant value, does xy have a maximum value or a minimum value? What is the maximum value equal to?
(2) When xy is a constant value, does x+y have a maximum value or a minimum value? What is the maximum value equal to?
Tips: Fill out the table. (1) When x+y is a fixed value, xy has a maximum value, and the maximum value is equal to
2. Fill in the blanks
Basic Inequalities and Maximum Values
It is known that x and y are both positive numbers.
3. Do it
It is known that x>0, y>0.
(1) If xy=4, then the minimum value of x+y is___________;
(2) If x+y=4, then the maximum value of xy is___________.
Basic Inequalities PPT, Part 3: Inquiry and Learning
Understanding basic inequalities
Example 1 Which of the following propositions is correct ()
Answer:B
Reflection: Pay attention to the following three points when applying basic inequalities.
(1) Each term or factor is positive;
(2) The sum or product is a constant value;
(3) Each term or factor can obtain equal values. That is, "one positive, two definite three are equal".
Variation Training 1 Which of the following conclusions is not true ()
A. If a,b∈R, then a10+b10≥2a5b5
D. If a∈R, then a2+9≥6a
Answer:C
Exploration 2 Use basic inequalities to prove inequalities
Example 2(1) It is known that a, b, c are not all equal positive real numbers,
Prove: a+b+c>√ab+√bc+√ca.
(2) It is known that a, b, c are positive real numbers, and a+b+c=1,
Verify: (1/a "-" 1)(1/b "-" 1)(1/c "-" 1)≥8.
Analysis: (1) The left side of the inequality is the sum, and the right side is the sum of the product expressions with the root sign. Use basic inequalities to convert the sum into the product, and prove the inequality. (2) The number on the right side of the inequality is 8, which reminds us By using basic inequalities for the factors on the left, we can get three consecutive multiplications of "2";
Basic Inequalities PPT, Part 4: Practice in class
1. It is known that x>0, then the minimum value of x+1/2x is ()
A.1/2 B.1 C.√2/2 D.√2
Analysis: From the basic inequality, we get x+1/2x≥2√(x"•" 1/2x)=√2. The equal sign holds true if and only if x=1/2x, that is, x=√2/2. Therefore, the minimum value is √2.
Answer:D
Keywords: Free download of PPT courseware for compulsory course I of mathematics version A of high school, basic inequalities PPT download, quadratic function equations and inequalities of one variable PPT download, .PPT format;
For more information about the PPT courseware "Quadratic Function Equations and Inequalities of One Variable and Basic Inequalities", please click the Basic Inequalities ppt tag of Quadratic Function Equations and Inequalities of One Variable.
"End of Chapter Review Lesson" Quadratic functions, equations and inequalities of one variable PPT:
"End of Chapter Review Lesson" Quadratic functions, equations and inequalities PPT reminds to explore the properties of inequalities [Example 1] If a, b, c satisfy c<b<a and ac<0, then one of the following options may not be true Yes ( ) A. ab>ac B. c(b-a)>0 C. cb2<ab..
"End of Chapter Review Improvement Course" Quadratic functions, equations and inequalities of one variable PPT:
"End of Chapter Review Improvement Course" Quadratic functions, equations and inequalities PPT of one variable comprehensively improves the application of the properties of inequalities (1) The following propositions are correct: ( ) ① If a1, then 1a1; ② If a+cb, then 1a1b; ③ For any real number a, both have a2a; ④If ac2bc2, then a...
"Quadratic Functions and Quadratic Equations and Inequalities" PPT courseware for quadratic functions, equations and inequalities (Lesson 2):
"Quadratic Functions and Quadratic Equations and Inequalities" PPT courseware for quadratic functions, equations and inequalities of one variable (Lesson 2) Part One Content: Learning Objectives 1. Master the practical application of quadratic inequalities of one variable (key points). 2. Understand The relationship between three quadratics. 3...
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