An inequality for a two variable function

In summary, an inequality is a mathematical expression that compares two quantities using symbols such as <, >, ≤, or ≥. It is different from an equation, which uses an equal sign (=) to show equality. An inequality for a two variable function is typically written in the form of f(x,y) < or > g(x,y), and its purpose is to show the relationship between two variables and determine the set of values that satisfy the inequality. To graph an inequality for a two variable function, points can be plotted on a coordinate plane and the region satisfying the inequality can be shaded.
  • #1
amirmath
8
0
Suppose that ##F(u,v)=a|u+v|^{r+1}+2b|uv|^{\frac{r+1}{2}}##, where ##a>1, b>0## and ##r\geq3.## How we can show that there exists a positive constant c such that
##
F(u,v)\geq c\Big( |u|^{r+1}+|v|^{r+1}\Big).
##
 
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  • #2
You'd start by considering what sort of curve is described by the part in parentheses in the second relation.
What role does c play? Is there a minimum value that the first expression can take?
 

Related to An inequality for a two variable function

1. What is an inequality?

An inequality is a mathematical expression that compares two quantities and indicates whether one is greater than, less than, or equal to the other.

2. How is an inequality different from an equation?

An inequality uses symbols such as <, >, ≤, or ≥ to compare two quantities, while an equation uses an equal sign (=) to show that two expressions are equal.

3. How is an inequality for a two variable function written?

An inequality for a two variable function is typically written in the form of f(x,y) < or > g(x,y), where f(x,y) and g(x,y) are two functions with x and y as variables.

4. What is the purpose of an inequality for a two variable function?

The purpose of an inequality for a two variable function is to show the relationship between two variables, and to determine the set of values that satisfy the inequality.

5. How do you graph an inequality for a two variable function?

To graph an inequality for a two variable function, you can plot points on a coordinate plane that satisfy the inequality and shade the region that represents the set of values that satisfy the inequality.

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