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The expression x to the power of 2 - 2mx has a minimum value as x varies Find the minimum value of x to the power of 2 - 2mx and Give your answer in terms of m?
If this is a homework question, please consider answering it on your own first, otherwise the value of the homework assignment, i.e. to reinforce the lesson, will be lost to you.
The minimum or maximum of a function y = f(x) can be found when the deriviative dy/dx f(x), or slope, is zero. In the case of a polynomial of degree two, which this question is, there is only one point where the deriviative is zero. In the general case of a polynomial of degree three or higher, however, any point where the slope is zero might only be a local minimum or maximum, so care must be taken. Also, you must always consider the second deriviative, in order to verify if that point is a minumum or a maximum.
The first deriviative of y = x2 - 2mx is 2x - 2m. (Remember, m is constant)
By simple algebra, the solution of 2x - 2m = 0 is x = m.
To determine if this is a minimum or a maximum, take the second deriviative.
The second deriviative of y = x2 - 2mx is the first deriviative of y = 2x - 2m, which is 2.
Since 2 is always positive, the slope is always increasing, so the point x = m is a minimum.
What else can I help you with?
What is the explanation for 10x plus 7 plus 3x?
The expression 10x + 7 + 3x can be simplified by combining like terms. Like terms are terms that have the same variable raised to the same power. In this case, the like terms are 10x and 3x, as they both have the variable x raised to the power of 1. Combining these like terms gives us 13x. Therefore, the simplified expression is 13x + 7.
What is an algebraic expression that has no like terms and no parentheses?
A simplified expression.
What is An expression of more than two algebraic terms?
It is an expression.
What is the definition of algebraic expression-?
Here is the correct defenition: Algebraic Expression is an expression which is obtained by performing a finite number of the following operations on symbols representing numbers: addition, subtraction, multiplication, division, raising to a power.
Examples of polynomials?
A polynomial is a function or expression that has two or more algebraic terms. Usually, each term has a different exponential power.
What is the expression for finding the minimum value of a function in terms of the variables g and l?
The expression for finding the minimum value of a function in terms of the variables g and l is typically written as f(g, l) minf(g, l).
What can blank an expression by combining blank which contains the same variable raised to the same power?
To simplify an expression, you can combine like terms, which contain the same variable raised to the same power. This process involves adding or subtracting the coefficients of those terms, resulting in a more concise expression. For example, in the expression (3x^2 + 5x^2), you can combine the terms to get (8x^2).
What terms are in the expression 3x to the second power plus 7x plus 1?
The three terms are 3x2, 7x and 1
What is x plus y to the 3rd power?
It's two terms of an algebraic expression.
What kind of terms may be added in an algebraic expression?
Similar terms. These are terms in which the variables have the same power in each term, and only the coefficient changes.
What is polynomia?
A polynomial is a math expression that has a sum of terms, each of the terms include a variable or variables multiplied by a coefficient and raised to a power.
Why does a quadratic expression have three terms if the prefix quad means four?
"Quadratic" in this sense means that the highest power used is two. This is similar to the use of "squared", for the power two. Since the highest power is two, you may need a term for the power two, a term for the power one, and a term for the power zero (the constant term). For comparison, a "cubic" expression means that the highest power that appears in an expression is the power 3.
X to the 3rd power -8?
x^3 -8 is two terms of an algebraic expression
How many terms are in a algebric expression?
An algebric expression can have any number of terms.
What is Multinomial?
multiterm mathematical expression: a mathematical expression consisting of the sum of a number of terms, each of which contains a constant and variables raised to a positive integral power
WhaT IS The addends of an algebraic expression?
are the terms of the expression
What are the terms in the expression 9h plus 13?
There are two terms in that expression. They are " 9h " and " 13 ".
