Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
![5. the sum of the squares of x and y
Example 3
Translate each mathematical phrase into verbal phrase.
x? +y2
1. 글x+ 1
1 added to - of a number x
4 is added to the product of 5
2. 5x+4
3. 3(x + 6)
4. x2 - 1
and a number x
thrice the sum of a number x and 6
1 subtracted from the square of a
number x
5. 7+
the sum of 7 and the quotient of x and 2
Activity 1
A. Translate each of the following mathematical phrases into verbal phrases.
6. 5x - 9y
7. 6x – 5
1. 4+3x
2. 3x-4
3. 2(x+ 3)
4. x-
8. (5 + x) + 2
9.2a + 3b
5. -5(4 + t)
10. 3 (3x + 8)
B. Translate each of the following into mathematical phrase.
1. the sum of x and y
2. twice the sum of a number and seven.
3. four increased by a certain number
4. the difference of five times a number and six.
5. thrice a number increased by five
e
Constant, Variables, Algebraic Expressions, Degree of Polynomial, and Kind of
Polynomial
This lesson introduces the terms
constant, variables, and algebraic expressions.
To better understand the lesson, let us describe the terms related to Algebra.
associated with algebra such
as
one or more than one value. These
Variables - are symbols or letters that may
variables may represent elements of the set of real numbers.
Constant- numbers or symbol which has a fixed numerical value.
For example: 2, 5, 0, -3, -7, etc. are constants.
In 2a, 2 is a constant and a is a variable.
In -7mn, -7 is a constant and m & n are variables.
Term - is a constant, a variable, or a product or a quotient of constants and
variables. Terms are separated by the symbols plus or minus sign.
3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5cb49120-411c-4c28-8747-e5f27a64a57c%2Fcf04e676-2c4b-4ca0-afa7-6f26bcf216ba%2Fllxcqd_processed.jpeg&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![Algebra and Trigonometry (6th Edition)](https://www.bartleby.com/isbn_cover_images/9780134463216/9780134463216_smallCoverImage.gif)
![Contemporary Abstract Algebra](https://www.bartleby.com/isbn_cover_images/9781305657960/9781305657960_smallCoverImage.gif)
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
![Algebra and Trigonometry (6th Edition)](https://www.bartleby.com/isbn_cover_images/9780134463216/9780134463216_smallCoverImage.gif)
![Contemporary Abstract Algebra](https://www.bartleby.com/isbn_cover_images/9781305657960/9781305657960_smallCoverImage.gif)
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
![Algebra And Trigonometry (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780135163078/9780135163078_smallCoverImage.gif)
![Introduction to Linear Algebra, Fifth Edition](https://www.bartleby.com/isbn_cover_images/9780980232776/9780980232776_smallCoverImage.gif)
![College Algebra (Collegiate Math)](https://www.bartleby.com/isbn_cover_images/9780077836344/9780077836344_smallCoverImage.gif)