Who created the leading coefficient test?
The leading coefficient test, also known as the leading term test, was not created by a specific individual. It is a concept in mathematics that has been developed and used by mathematicians over time. The leading coefficient test is a method used to determine the end behavior of a polynomial function.
To understand the leading coefficient test, you need to know the following:
1. Polynomial: A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, but not division or exponentiation. Examples of polynomials include 2x^2 - 3x + 1 and x^3 + 4x^2 - 2x + 5.
2. Leading Term: In a polynomial, the term with the highest degree is called the leading term. The degree of a term is the exponent of the variable. For example, in the polynomial 2x^3 - 5x^2 + 3x - 1, the leading term is 2x^3, which has a degree of 3.
3. Leading Coefficient: The coefficient of the leading term is known as the leading coefficient. In the example polynomial above, the leading coefficient is 2.
Now, to apply the leading coefficient test:
1. If the leading coefficient of a polynomial is positive, then the polynomial will have the same end behavior as a positive power function. This means that as x approaches positive or negative infinity, the function will either increase or decrease without bound, respectively.
2. If the leading coefficient of a polynomial is negative, then the polynomial will have the opposite end behavior of a positive power function. This means that as x approaches positive or negative infinity, the function will either decrease or increase without bound, respectively.
So, to determine who created the leading coefficient test, it is not attributed to a single person since it is a concept that has evolved and been used in mathematics over time.