Python-Sympy最小值和最大值

Question

我正在嘗試學習sympy的微積分函數，並且能夠通過以下方式獲得關於極值臨界點的二階導數的根：

import numpy as np
    from numpy import linspace, math, arange, linspace
    from sympy import *
    import sympy as sp
    import math

    x = Symbol('x')
    f = (x**4) - (24*x**2) + 80  
    fd = diff(f)
    fdd = diff(fd)
    print(fd)
    print(fdd)

    polyRoots = solveset(f,x)
    dRoots = solveset(fd,x) #gets critical x values
    ddRoots = solveset(fdd,x)

如何將從dRoots獲得的值替換為原始方程式f，並使其輸出值列表？

Answer 1

>>> from sympy import *
>>> x = Symbol('x')
>>> f = x**4 - 24*x**2 + 80
>>> fd = diff(f)
>>> fdd = diff(fd)
>>> polyRoots = solveset(f, x)
>>> dRoots = solveset(fd, x)
>>> ddRoots = solveset(fdd, x)
>>> dRoots
{0, -2*sqrt(3), 2*sqrt(3)}
>>> [_ for _ in dRoots]
[0, -2*sqrt(3), 2*sqrt(3)]
>>> [f.subs(x, _) for _ in dRoots]
[80, -64, -64]

您可以通過執行以下操作來驗證這是否有意義：

>>> [f.subs(x, _) for _ in polyRoots]
[0, 0, 0, 0]