titled

566014.7604 6575670.0925 52.5728
566016.8032 6575663.6837 51.9256
566018.8461 6575657.2748 51.3135
566020.8889 6575650.8659 50.7367
566022.9318 6575644.4571 50.1951
566024.9746 6575638.0482 49.6888
566027.0175 6575631.6394 49.2176
566029.0603 6575625.2305 48.7816
566031.1032 6575618.8216 48.3808
566033.1460 6575612.4128 48.0153
566035.1888 6575606.0039 47.6849
566037.2317 6575599.5950 47.3898
566039.2745 6575593.1862 47.1298
566041.3174 6575586.7773 46.9051
566043.3602 6575580.3684 46.7155
566045.4031 6575573.9596 46.5612
566047.4459 6575567.5507 46.4421
566049.4888 6575561.1418 46.3582
566051.5316 6575554.7330 46.3095
566053.5745 6575548.3241 46.2960
566055.6173 6575541.9152 46.3177
566057.6602 6575535.5064 46.3746
566059.7030 6575529.0975 46.4667
566061.7459 6575522.6886 46.5940
566063.7887 6575516.2798 46.7566
566065.8315 6575509.8709 46.9543
566067.8744 6575503.4620 47.1873
566069.9172 6575497.0532 47.4554
566071.9601 6575490.6443 47.7588
566074.0029 6575484.2354 48.0973
566076.0458 6575477.8266 48.4711
566078.0886 6575471.4177 48.8801
566080.1315 6575465.0088 49.3242
566082.1743 6575458.6000 49.8036
566084.2172 6575452.1911 50.3182
566086.2600 6575445.7823 50.8680
566088.3029 6575439.3734 51.4530
566090.3457 6575432.9645 52.0732
566092.3886 6575426.5557 52.7287
566094.4450 6575420.1510 53.4190

import sympy as sp
import numpy as np
from IPython.display import display
import matplotlib.pyplot as plt
#init_printing(use_unicode=False, wrap_line=False, no_global=True)
x,x0,y0,A=sp.symbols('x x_0 y_0, A', real=True)
sp.init_printing()

expr=(A*sp.cosh((x-x0)/A)+y0-A)**2
new_expr=(A*(sp.exp((x-x0)/A)+sp.exp(-(x-x0)/A))/2+y0-A)**2
diff_of_expr=sp.simplify(sp.diff(expr, x))
diff_of_new_expr=sp.simplify(sp.diff(new_expr, x))
solution=sp.solvers.solve(diff_of_expr, x)

print('DERIVATIVE OF')
display(expr)
print('OR alternatively')
display(new_expr)
print('IN x IS:')
display(diff_of_expr)
print('OR alternatively:')
display(diff_of_new_expr)
#sp.nonlinsolve has lost
print('ROOTS OF THIS EXPRESSION IS:')
display(solution)
print('THIS EXPRESSIONS IS WHAT WE''VE GOT SETTING SOLUTIONS INTO EXPRESSION:')
print('-'*80)
for n in solution:
    display(diff_of_expr.subs(x, n))
    print('AFTER SIMPLIFICATIONS:')
    display(sp.simplify(diff_of_expr.subs(x, n)))
    if not(sp.simplify(diff_of_expr.subs(x, n))==0):
        print('TRYING TO RESOLVE:')
        display(sp.simplify(diff_of_new_expr.subs(x, n)))
    print('-'*80)
#solution must return minimum value of x
'''
s=np.linspace(0,4,100)
_x0,_y0,_A=2,3,1
plt.plot(s,_A*np.cosh((s-_x0)/_A)+_y0-_A)
_A=2
plt.plot(s,_A*np.cosh((s-_x0)/_A)+_y0-_A)
_A=3
plt.plot(s,_A*np.cosh((s-_x0)/_A)+_y0-_A)
plt.show()'''