I$\text{'}$m trying to use the following code to answer $4$ numerical analysis questions. Each question should have its own cell and a visual representation like the one screenshot. This is in python.

# The following code finds the forward, backward, and centered differencevalues, then plots the absolute errors on a log$-$Log scale plot.$\backslash$import numpy as np

import matplotlib.pyplot as plt$\%$matplotlib inlinePoint where derivative is evaluated

x$=0\mathrm{.}5$

#function to be differentiated

f$=$np$.$exp$($x$)$

#Derivative of function $($theo$.$ calculation$)$

fPrime$=$np$.$exp$($x$)$

#get vector of deltax values

deltax $=2.**$np$.$arange$(-1,-14,-1)$#Compute forward approx.

fPlus $=$ np$.$exp$($x$+$deltax$)$

forward $=($fPlus$-$f$)/$deltax

#Compute backward approx

fMinus $=$ np$.$exp$($x$-$deltax$)$

backward $=($f$-$fMinus$)/$deltax

#use average of forward and backward for centered

centered $=($forward $+$ backward$)\}/$

#compute absolute errors

forwardError $=$ abs$($fPrime $-$ forward$)$

backwardError $=$ abs$($fPrime $-$ backward$)$

centerError $=$ abs$($fPrime $-$ centered$)$plt$.$figure$(1)$

#plot forward, backward, and centered errors on log$-$log scale

plt$.$plot$($deltax$,$ forwardError, label$=$"Forward Difference"$)$

plt$.$plot$($deltax$,$ backwardError, label$=$"Backward Difference"$)$

plt$.$plot$($deltax$,$ centerError, label$=$"Centered Difference"$)$plt$.$xlim$([1,1$e$-4])$

plt$.$ylim$([1$e$-9,1])$plt$.$xscale$("$log$")$

plt$.$yscale$("$log$")$plt$.$xlabel$("$Delta x$")$

plt$.$ylabel$("$Absolute Error"$)$ #Compute forward approx.

fPlus $=$ np$.$exp$($x$+$deltax$)$

forward $=($fPlus$-$f$)/$deltax

#Compute backward approx

fMinus $=$ np$.$exp$($x$-$deltax$)$

backward $=($f$-$fMinus$)/$deltax

#use average of forward and backward for centered

centered $=($forward $+$ backward$)/2$

#compute absolute errors

forwardError $=$ abs$($fPrime $-$ forward$)$

backwardError $=$ abs$($fPrime $-$ backward$)$

centerError $=$ abs$($fPrime $-$ centered$)$plt$.$figure$(1)$

#plot forward, backward, and centered errors on log$-$log scale

plt$.$plot$($deltax$,$ forwardError, label$=$"Forward Difference"$)$

plt$.$plot$($deltax$,$ backwardError, label$=$"Backward Difference"$)$

plt$.$plot$($deltax$,$ centerError, label$=$"Centered Difference"$)$plt$.$xlim$([1,1$e$-4])$

plt$.$ylim$([1$e$-9,1])$plt$.$xscale$("$log$")$

plt$.$yscale$("$log$")$plt$.$xlabel$("$Delta x$")$

plt$.$ylabel$("$Absolute Error"$)$plt$.$ legend$($loc$=3)$

plt$.$title$("$Errors for Fw$,$ Bw$,$ Ct Difference approx for $f(x)=e^x")$

plt$.$show$()$