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Tangent Lines and Derivatives definitions

1 학생이 이 점이 도움이 되었다고 느꼈습니다
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  • Secant Line
    A straight path intersecting a curve at two distinct points, used to find average rate of change.
  • Tangent Line
    A straight path touching a curve at exactly one point, representing instantaneous rate of change.
  • Slope
    A measure of steepness for a line, calculated as the ratio of vertical to horizontal change.
  • Limit
    A mathematical process describing the value a function approaches as the input nears a specific point.
  • Derivative
    A value representing the instantaneous rate of change of a function at a specific input.
  • Point-Slope Form
    An equation format for a line using a known point and the line's slope to express its relationship.
  • Difference of Squares
    An algebraic expression of the form a^2 - b^2, which factors into (a + b)(a - b).
  • Indeterminate Form
    An expression like 0/0, which lacks a defined value and requires algebraic manipulation to resolve.
  • Average Rate of Change
    A value describing how a function changes between two points, found using a secant line.
  • Instantaneous Rate of Change
    A value describing how a function changes at a single point, found using a tangent line or derivative.
  • Function
    A rule assigning each input exactly one output, often written as f(x).
  • Factoring
    A process of rewriting an expression as a product of simpler expressions, often to simplify limits.
  • Cancellation
    A simplification step where common factors in the numerator and denominator are removed.
  • Numerator
    The top part of a fraction, representing the quantity being divided.
  • Denominator
    The bottom part of a fraction, indicating the number of equal parts the whole is divided into.