#範例5-4：求一階導數，判別局部極大值，極小值的位置
from sympy import *
x = symbols('x')
y = Function('y')(x)
y = sqrt(3)*cos(x) + sin(x) + 1
#求f的局部極值（極大值，極小值）
dif1y = diff(y, x, 1)
print('一階導數函數 = ', dif1y)
#求解一階導數=0的位置
print('求解一階導數=0的解 = ', solve(dif1y,x))
#兩個解，x0,x1
x0 = solve(dif1y,x)[0]
x1 = solve(dif1y,x)[1]
print(x0,x1)

#判別斜率正負
if dif1y.subs(x,x0-0.1) < 0 and dif1y.subs(x,x0+0.1) > 0:
    print('x=',x0,'的位置是局部最小值')
elif dif1y.subs(x,x0-0.1) >0 and dif1y.subs(x,x0+0.1) <0:
    print('x=',x0,'的位置是局部最大值')

if dif1y.subs(x,x1-0.1) < 0 and dif1y.subs(x,x1+0.1) > 0:
    print('x=',x1,'的位置是局部最小值')
elif dif1y.subs(x,x1-0.1) >0 and dif1y.subs(x,x1+0.1) <0:
    print('x=',x1,'的位置是局部最大值')
    
#畫出y的線性
plot(y, line_color='red')