Minimizing a function in python

[ver_mathstats]

The function is f(x)=x⁵-12x³+7x²+2x+7.

I found the minimum of the function and compared the value to a calculator and it seemed okay. But I am confused as to how to incorporate the interval into my code. Has my code already sufficiently answered the question?

from scipy import optimize
import numpy as np
import matplotlib.pyplot as plt 

def f(x):
    return (x**5)-12*(x**3)+7*(x**2)+2*x+7

xdom=np.linspace(-2,2,1000)
plt.plot(xdom,f(xdom))

minimum=optimize.fmin(f,1)
print('The minimum:',minimum)

Thank you.

 

[Mark44]

Homework Statement:: Minimize the function on the interval [0,infinity).
Relevant Equations:: Python

The function is f(x)=x⁵-12x³+7x²+2x+7.

I found the minimum of the function and compared the value to a calculator and it seemed okay. But I am confused as to how to incorporate the interval into my code. Has my code already sufficiently answered the question?

from scipy import optimize
import numpy as np
import matplotlib.pyplot as plt

def f(x):
    return (x**5)-12*(x**3)+7*(x**2)+2*x+7

xdom=np.linspace(-2,2,1000)
plt.plot(xdom,f(xdom))

minimum=optimize.fmin(f,1)
print('The minimum:',minimum)

Thank you.

I would get creative. Your function, $f(x) = x^5 - 12x^3 + 7x^2 + 2x + 7$ is dominated by the 5th degree term. Just in round number, $6^5$ is more positive than $-12*6^3$, and the other terms are pretty much insignificant. Obviously, you can't have an interval that stretches from 0 to infinity, so the function should be positive and increasing steadily if $x \ge 10$, just to pick a number.

I see that your interval is [-2, 1000] in increments of 2. With a smaller interval and finer increments, you should be able to get a better estimate of the minimum value. Otherwise, it looks like you're on the right track.

 

[ver_mathstats]

I would get creative. Your function, $f(x) = x^5 - 12x^3 + 7x^2 + 2x + 7$ is dominated by the 5th degree term. Just in round number, $6^5$ is more positive than $-12*6^3$, and the other terms are pretty much insignificant. Obviously, you can't have an interval that stretches from 0 to infinity, so the function should be positive and increasing steadily if $x \ge 10$, just to pick a number.

I see that your interval is [-2, 1000] in increments of 2. With a smaller interval and finer increments, you should be able to get a better estimate of the minimum value. Otherwise, it looks like you're on the right track.

Oh okay, that all makes sense. Thank you for the response.