Quadratic Derivatives

quadratic_derivatives(first_constant, second_constant, third_constant, precision=4)

Calculates the first and second derivatives of a quadratic function

Parameters

  • first_constant (int or float) – Coefficient of the quadratic term of the original quadratic function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

  • second_constant (int or float) – Coefficient of the linear term of the original quadratic function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

  • third_constant (int or float) – Coefficient of the constant term of the original quadratic function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

  • precision (int, default=4) – Maximum number of digits that can appear after the decimal place of the resultant roots

Raises

  • TypeError – First three arguments must be integers or floats

  • ValueError – Last argument must be a positive integer

Returns

  • derivatives[‘first’][‘constants’] (list of float) – Coefficients of the resultant first derivative

  • derivatives[‘first’][‘evaluation’] (func) – Function for evaluating the resultant first derivative at any float or integer argument

  • derivatives[‘second’][‘constants’] (list of float) – Coefficients of the resultant second derivative

  • derivatives[‘second’][‘evaluation’] (func) – Function for evaluating the resultant second derivative at any float or integer argument

See also

quadratic_equation(), quadratic_integral(), quadratic_roots(), quadratic_model()

Notes

  • Standard form of a quadratic function: \(f(x) = a\cdot{x^2} + b\cdot{x} + c\)

  • First derivative of a quadratic function: \(f'(x) = 2a\cdot{x} + b\)

  • Second derivative of a quadratic function: \(f''(x) = 2a\)

  • Basic Differentiation Forumulas

Examples

Import quadratic_derivatives function from regressions library
>>> from regressions.analyses.derivatives.quadratic import quadratic_derivatives
Generate the derivatives of a quadratic function with coefficients 2, 3, and 5, then display the coefficients of its first and second derivatives
>>> derivatives_constants = quadratic_derivatives(2, 3, 5)
>>> print(derivatives_constants['first']['constants'])
[4.0, 3.0]
>>> print(derivatives_constants['second']['constants'])
[4.0]
Generate the derivatives of a quadratic function with coefficients 7, -5, and 3, then evaluate its first and second derivatives at 10
>>> derivatives_evaluation = quadratic_derivatives(7, -5, 3)
>>> print(derivatives_evaluation['first']['evaluation'](10))
135.0
>>> print(derivatives_evaluation['second']['evaluation'](10))
14.0
Generate the derivatives of a quadratic function with all inputs set to 0, then display the coefficients of its first and second derivatives
>>> derivatives_zeroes = quadratic_derivatives(0, 0, 0)
>>> print(derivatives_zeroes['first']['constants'])
[0.0002, 0.0001]
>>> print(derivatives_zeroes['second']['constants'])
[0.0002]