[FIXED] How to find minima and maxima of a function. I am limited to using numpy, sympy and matplotlib

Issue

I am asked to find the maxima and minima of few functions. One of the functions is y = (9x^3) - (7x^2) + (3x) + 10 The code I could write so far is:

from sympy import*
import matplotlib.pyplot as plt

x = symbols ('x')
f = (9*x**3) - (7*x**2) + (3*x) + 10

intervals = np.arange(-5, 7)

df = diff(f, x)
df2 = diff(f, x, 2)

f = lambdify (x, f)
y = f(intervals)

print (intervals)
print (y)

I am new to using these 3 libraries so I dont know how to find the answer using these 3 libraries

Solution

SymPy can tell you the derivative and f and can tell you when a function is zero. Since max/min occur when the derivative is zero you can find the zeros and then determine if those values make the 2nd derivative positive or negative, e.g.

>>> from sympy import real_roots
>>> from sympy.abc import x
>>> f = -x**2 + 1
>>> d1 = f.diff(x)
>>> d2 = d1.diff(x)  # = f.diff(x,2)
>>> extrema = real_roots(d1)
>>> for i in extrema:
...   if d2.subs(x, i).is_positive:
...      print('minimum',i)
...   else:
...      print('maxima',i)

See also here. (If there are no real roots then there are no extrema for real values of x.)

Answered By - smichr