How can this code be extended to display the information on a graph?

import numpy as np

# Define the function based on the equation: f$($x$)=$ ax$^$b $-$ e$^($cx$)*$ sin$($wx $+$ v$)$

def f$($x$,$ a$,$ b$,$ c$,$ w$,$ v$)$:

$$ return a $*$ x$**$b $-$ np$.$exp$($c $*$ x$)*$ np$.$sin$($w $*$ x $+$ v$)$

# Define the derivative of the function with respect to x$,$ which is required for Newton's method

def f$\_$prime$($x$,$ a$,$ b$,$ c$,$ w$,$ v$)$:

$$ term$1=$ b $*$ a $*$ x$**($b $-1)$# Derivative of ax$^$b

$$ term$2=$ np$.$exp$($c $*$ x$)*($c $*$ np$.$sin$($w $*$ x $+$ v$)+$ w $*$ np$.$cos$($w $*$ x $+$ v$))$# Derivative of e$^($cx$)*$ sin$($wx $+$ v$)$

$$ return term$1-$ term$2$

# Function implementing Newton's method to find a root starting from an initial guess x$0$

def newtons$\_$method$($a$,$ b$,$ c$,$ w$,$ v$,$ x$0,$ tolerance$=1$e$-7,$ max$\_$iterations$=100)$:

$$ x $=$ x$0$

$$ for i in range$($max$\_$iterations$)$:

$$ fx $=$ f$($x$,$ a$,$ b$,$ c$,$ w$,$ v$)$# Evaluate the function at current x

$$ fpx $=$ f$\_$prime$($x$,$ a$,$ b$,$ c$,$ w$,$ v$)$# Evaluate the derivative at current x

$$ # Check if derivative is zero to avoid division by zero

$$ if fpx $==0$:

$$ print$("$Zero derivative. No solution found."$)$

$$ return None

$$ # Update x using Newton's formula

$$ x$\_$new $=$ x $-$ fx $/$ fpx

$$ # Check for convergence within the specified tolerance

$$ if abs$($x$\_$new $-$ x$)<$ tolerance:

$$ return x$\_$new $$# Return the converged solution

$$ # Update x to the new value for the next iteration

$$ x $=$ x$\_$new

$$ # If the loop completes without convergence, print a message

$$ print$("$Exceeded maximum iterations. No solution found."$)$

$$ return None

# Function to find multiple roots by applying Newton's method from various initial guesses

def find$\_$multiple$\_$solutions$($a$,$ b$,$ c$,$ w$,$ v$,$ initial$\_$guesses$)$:

$$ solutions $=[]$

$$ for x$0$ in initial$\_$guesses:

$$ solution $=$ newtons$\_$method$($a$,$ b$,$ c$,$ w$,$ v$,$ x$0)$

$$ # If a valid solution is found, check if it's unique before adding to the list

$$ if solution is not None:

$$ if all$($abs$($solution $-$ s$)>1$e$-5$ for s in solutions$)$:

$$ solutions.append$($solution$)$

$$ return solutions

# Example usage with parameters a$,$ b$,$ c$,$ w$,$ v$,$ and a list of initial guesses

a$,$ b$,$ c$,$ w$,$ v $=1,2,-0\mathrm{.}5,1\mathrm{.}5,0\mathrm{.}5$

initial$\_$guesses $=[-10,-5,0,5,10]$# Varied starting points to find multiple solutions

# Run the function and print the found solutions

solutions $=$ find$\_$multiple$\_$solutions$($a$,$ b$,$ c$,$ w$,$ v$,$ initial$\_$guesses$)$

print$("$Found solutions:", solutions$)$