 # and 2) illustrate results graphically.

import numpy
import math
from numpy import arange, cos
import matplotlib.pyplot
from matplotlib.pyplot import *

# x+delta.

def der(x,delta):
delta = float(delta)
if delta < (0.0000001):
print (‘Value chosen for delta is too small.’)
return 1/delta
else:
slope = (f(x + delta) - f(x))/delta
return slope

# Define the function y=100e^(-0.0482t)

def f(x):
f = (100.0**(-0.0482*x))
return f

point = 2.0 #This is a point at which a derivative will be calculated.

# The following statements initialize variables for computation.

number = 510
increment =10
y =
x =

figure()
f=[3,-4,-12,0,2]
print (’\nFunction’)
print f

print (’\nFirst Derivative’)
g= f.deriv(m=1) # First derivative with m=1.
print g

print (’\nSecond Derivative’)
q= f.deriv(m=2) # Second derivative with m=2.
print q

x=linspace(-2,3,101)
y=p(x)
yg=g(x) # These statements define points for plotting.
yq=q(x)
y0=0*x # This statement defines the y axis for plotting.

plot (x,y,label =‘y=f(x)’)
plot (x,yg,label =‘First Derivative’)
plot (x,yq,label =‘Second Derivative’)
legend(loc=‘best’)

plot (x,y0)
xlabel(‘x-axis’)
ylabel(‘y-axis’)
title (‘Plot Showing Function, First and Second Derivatives’)
show()

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``````# objectives: 1) demonstrate numerical differentialtion,
# and 2) illustrate results graphically.

import numpy
import math
from numpy import arange, cos
import matplotlib.pyplot
from matplotlib.pyplot import *

# A general function for calculating the slope between two points: x and
# x+delta.

def der(x,delta):
delta = float(delta)
if delta < (0.0000001):
print ('Value chosen for delta is too small.')
return 1/delta
else:
slope = (f(x + delta) - f(x))/delta
return slope

# Define the function y=100e^(-0.0482t)

def f(x):
f = (100.0**(-0.0482*x))
return f

point = 2.0  #This is a point at which a derivative will be calculated.
# The following statements initialize variables for computation.

number = 510
increment =10
y = []
x = []

figure()
f=[3,-4,-12,0,2]
print ('\nFunction')
print f

print ('\nFirst Derivative')
g= f.deriv(m=1) # First derivative with m=1.
print g

print ('\nSecond Derivative')
q= f.deriv(m=2) # Second derivative with m=2.
print q

x=linspace(-2,3,101)
y=p(x)
yg=g(x) # These statements define points for plotting.
yq=q(x)
y0=0*x # This statement defines the y axis for plotting.

plot (x,y,label ='y=f(x)')
plot (x,yg,label ='First Derivative')
plot (x,yq,label ='Second Derivative')
legend(loc='best')

plot (x,y0)
xlabel('x-axis')
ylabel('y-axis')
title ('Plot Showing Function, First and Second Derivatives')
show()``````