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Antiderivatives definitions

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  • Antiderivative
    Reverse process of differentiation, yielding a function whose derivative matches the given function.
  • Derivative
    Result of applying differentiation, representing the rate of change or slope of a function.
  • Constant of Integration
    Unknown value added to an antiderivative, accounting for any constant lost during differentiation.
  • General Antiderivative
    Family of functions differing by a constant, all having the same derivative as the original function.
  • Particular Antiderivative
    Unique function from the general family, determined by an initial condition or given point.
  • Power Rule
    Technique for finding derivatives or antiderivatives involving exponents, simplifying polynomial expressions.
  • Vertical Shift
    Graph movement up or down, represented by the constant in the antiderivative.
  • Initial Condition
    Given value for a function at a specific point, used to solve for the constant in an antiderivative.
  • Family of Functions
    Set of functions differing only by a constant, all sharing the same derivative.
  • Function Notation
    Symbolic representation such as f(x) or F(x), distinguishing between original and antiderivative functions.
  • Checking Solution
    Process of differentiating an antiderivative to verify it returns the original function.
  • Polynomial
    Expression involving terms with variables raised to whole-number exponents, often used in antiderivative examples.
  • Graph
    Visual representation of a function, illustrating the effect of the constant in antiderivatives.
  • Output Value
    Result of substituting a specific input into a function, used to determine the constant in a particular antiderivative.