+---+------+---------+----+----+--------+---------+------+------+---------+---------+
    | :ref:`brentq <optimize.root_scalar-brentq>`   | x |  o   |    x    |    |    |        |         |  o   |  o   |    o    |   o     |
    +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+
    | :ref:`brenth <optimize.root_scalar-brenth>`   | x |  o   |    x    |    |    |        |         |  o   |  o   |    o    |   o     |
    +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+
    | :ref:`ridder <optimize.root_scalar-ridder>`   | x |  o   |    x    |    |    |        |         |  o   |  o   |    o    |   o     |
    +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+
    | :ref:`toms748 <optimize.root_scalar-toms748>` | x |  o   |    x    |    |    |        |         |  o   |  o   |    o    |   o     |
    +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+
    | :ref:`secant <optimize.root_scalar-secant>`   | x |  o   |         | x  | o  |        |         |  o   |  o   |    o    |   o     |
    +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+
    | :ref:`newton <optimize.root_scalar-newton>`   | x |  o   |         | x  |    |   o    |         |  o   |  o   |    o    |   o     |
    +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+
    | :ref:`halley <optimize.root_scalar-halley>`   | x |  o   |         | x  |    |   x    |    x    |  o   |  o   |    o    |   o     |
    +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+

    Examples
    --------

    Find the root of a simple cubic

    >>> from scipy import optimize
    >>> def f(x):
    ...     return (x**3 - 1)  # only one real root at x = 1

    >>> def fprime(x):
    ...     return 3*x**2

    The `brentq` method takes as input a bracket

    >>> sol = optimize.root_scalar(f, bracket=[0, 3], method='brentq')
    >>> sol.root, sol.iterations, sol.function_calls
    (1.0, 10, 11)

    The `newton` method takes as input a single point and uses the
    derivative(s).

    >>> sol = optimize.root_scalar(f, x0=0.2, fprime=fprime, method='newton')
    >>> sol.root, sol.iterations, sol.function_calls
    (1.0, 11, 22)

    The function can provide the value and derivative(s) in a single call.

    >>> def f_p_pp(x):
    ...     return (x**3 - 1), 3*x**2, 6*x

    >>> sol = optimize.root_scalar(
    ...     f_p_pp, x0=0.2, fprime=True, method='newton'
    ... )
    >>> sol.root, sol.iterations, sol.function_calls
    (1.0, 11, 11)

    >>> sol = optimize.root_scalar(
    ...     f_p_pp, x0=0.2, fprime=True, fprime2=True, method='halley'
    ... )
    >>> sol.root, sol.iterations, sol.function_calls
    (1.0, 7, 8)


    NFT)