뒤로Tangent Lines & Derivatives definitions
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1/15뒤로Skip to main content뒤로Tangent Line
A straight line that touches a curve at exactly one point, representing the instantaneous direction of the curve at that point. Secant Line
A straight line that intersects a curve at two distinct points, representing the average rate of change between those points. Point of Tangency
The specific location on a curve where a tangent line touches, corresponding to a single x-value of interest. Slope
A measure of steepness of a line, calculated as the ratio of vertical change to horizontal change between two points. Limit
A mathematical concept describing the value a function approaches as the input approaches a specific point. Difference of Squares
An algebraic expression of the form a^2 - b^2, which factors into (a + b)(a - b). Derivative
A function that gives the slope of the tangent line to a curve at any point, representing instantaneous rate of change. Instantaneous Rate of Change
The rate at which a function changes at a single point, found using the slope of the tangent line. Average Rate of Change
The change in a function's value over an interval, calculated using the slope of a secant line. Point-Slope Form
An equation format for a line using a known point and the slope, typically written as y - y₁ = m(x - x₁). Prime Notation
A shorthand symbol (') used to denote the derivative of a function, such as f'(x). Limit Definition of Derivative
A formula expressing the derivative as the limit of the difference quotient as the interval approaches zero. Difference Quotient
An expression representing the average rate of change of a function over an interval, used in the definition of the derivative. Function Notation
A way to represent functions, typically written as f(x), indicating the output for a given input x. Factoring
An algebraic process of rewriting an expression as a product of its simpler components, often used to simplify limits.
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