Lab 8: Solving Various Types of Inequalities

These flashcards cover key vocabulary and concepts related to solving inequalities, derivatives, and analysis of functions as discussed in Lab 8.

Inequality

A mathematical statement that compares two expressions, indicating whether one is less than, greater than, or not equal to the other.

Critical Number

A number in the domain of a function where the derivative is zero or undefined.

Test Value

A number chosen from each interval to determine whether the function is positive or negative.

Positive Interval

An interval where the function's output is greater than zero.

Negative Interval

An interval where the function's output is less than zero.

Parabola

A symmetrical open plane curve formed by the intersection of a right circular conical surface and a plane parallel to an element of the curve.

Derivative

A measure of how a function changes as its input changes, usually represented as f'(x) or dy/dx.

Polynomial Inequality

An inequality that involves a polynomial expression, often requiring solving the corresponding polynomial equation first.

Interval Notation

A mathematical notation used to represent a set of numbers between two endpoints.

Number Line

A line used to represent real numbers, where each point on the line corresponds to a unique real number.

Sign Chart

A visual representation used to determine where a function is positive or negative based on test values in intervals.

Algebraic Expression

A mathematical phrase that can include numbers, variables, and operations, but does not have an equality sign.