Question

Consider the following function with a real variable, x:
?(?) = ?³ - 3?² + 6? + 10
a. Write a Python function for the derivative of f(x) that takes x and returns the derivative of f(x). Take the derivative of f(x) analytically with respect to x before writing the function.

b. Write a Python code that approximately finds the real root, x0, of f(x) such that f(x0)~0 using the Newton-Raphson method. The code is expected to get an initial guess from a user using the input statement. At each iteration, the code is expected to print the iteration number, the new guess and the absolute value of f(x) at the guess. Iterations should stop when the absolute value of f(x) at the guess is less than 10^-6.
Hint: Use a while loop to implement the Newton-Raphson method where each execution of the loop corresponds to an iteration. At each iteration, find a new guess for that iteration using the iterative expression for the Newton-Raphson method.

Answer 1

`Hey,

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https://trinket.io/python3/331d3c0b37

def func( x ):
return x * x*x-3*x*x+6*x+10
# Derivative of the above function
# which is 3*x^x - 2*x
def derivFunc( x ):
return 3*x*x-6*x+6
  
# Function to find the root
def newtonRaphson( x ):
h = func(x) / derivFunc(x)
while abs(func(x)) >= 1e-6:
h = func(x)/derivFunc(x)
# x(i+1) = x(i) - f(x) / f'(x)
x = x - h
  
print("The value of the root is : ",
"%.4f"% x)
  
# Driver program to test above
x0 =int(input("Enter initial guess: "));
newtonRaphson(x0)

Kindly revert for any queries

Thanks.