import numpy as np

# Define the function g$($t$)$

def g$($t$)$:

return $336*$ t$**5-1740*$ t$**4+3204*$ t$**3-34992*$ t$**2+34992*$ t

# Define the initial interval $[$a$,$ b$]$

a $=5$

b $=8$

# Initialize c$1$ using the secant method formula

c$1=($a $*$ g$($b$)-$ b $*$ g$($a$))/($g$($b$)-$ g$($a$))$

# Set the tolerance for convergence

tolerance $=$ np$.$abs$($c$1-$ a$)$

# Iteratively apply the secant method

while tolerance $>=0\mathrm{.}001$:

# Check if g$($c$1)$ is not zero to avoid division by zero

if g$($c$1)==0$:

break

# Update interval $[$a$,$ b$]$ based on the function values

if g$($c$1)*$ g$($a$)>0$:

a $=$ c$1$

else:

b $=$ c$1$

# Compute the new c$2$ using the secant method formula

c$2=($a $*$ g$($b$)-$ b $*$ g$($a$))/($g$($b$)-$ g$($a$))$

# Update tolerance and c$1$

tolerance $=$ np$.$abs$($c$2-$ c$1)$

c$1=$ c$2$

# Print the final result

print$($c$1)$