Get minimum point(s) of numpy.poly1d curve

Question

I have a numpy.poly1d polynomial as follows:

c = np.poly1d([2,-4,-28,62,122,-256,-196,140,392,240,72])

The curve looks like this when graphed in the range -2.5 <= x <= 2.5:

How can I find the minimum point(s) of this curve within the given range, without using the discrete values used to graph the curve (by this I mean using only the continuous poly1d object)?

Answer 1

OK a bit different functions than @matiasg aim is to make more copyable code and use as much vectorized code as possible.

import numpy as np
from matplotlib.pyplot import *

c = np.poly1d([2,-4,-28,62,122,-256,-196,140,392,240,72])

crit = c.deriv().r
r_crit = crit[crit.imag==0].real
test = c.deriv(2)(r_crit) 


# compute local minima 
# excluding range boundaries
x_min = r_crit[test>0]
y_min = c(x_min)
plot( x_min, y_min, 'o' )

xc = np.arange(-2.5, 2.6, 0.02)
yc = c(xc)
plot( xc, yc)

xlim([-2.5,2.5])
show()

Image 1: Result. Note there is another local minima just outside your bounds ;)