Write an algorithm out in plain language (not MATLAB), but with mathematical notation that incrementally searches for intervals containing possible roots of a function. Consider both the sign of the function and the sign of the first derivative. Note, you are not trying to exactly determine the roots through a root finding algorithm, but rather trying to identify possible root containing regions by examining the shape of the function.
Solution
## assuming root is in positive side
x_start=0
dx=0.001 ## increment
i=0
while i<=2000:# to check till 2000 iterations
if f(x_start)==0:
break
print (\'root is\', x_start)
elif:
f(x_start)/f(x_start+dx)<0:# negative sign means root lies b/w
print (\'root lies b/w\', x_start,\'and\',x_start+dx)
break
else:
x_start=x_start+dx
i=i+1
if i==2000:
print (\'root does not lie b/w zero and\',x_start+i*dx)
## it is algorithm in python
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Write an algorithm out in plain language (not MATLAB)- but with mathem.docx
1. Write an algorithm out in plain language (not MATLAB), but with mathematical notation that
incrementally searches for intervals containing possible roots of a function. Consider both the
sign of the function and the sign of the first derivative. Note, you are not trying to exactly
determine the roots through a root finding algorithm, but rather trying to identify possible root
containing regions by examining the shape of the function.
Solution
## assuming root is in positive side
x_start=0
dx=0.001 ## increment
i=0
while i<=2000:# to check till 2000 iterations
if f(x_start)==0:
break
print ('root is', x_start)
elif:
f(x_start)/f(x_start+dx)<0:# negative sign means root lies b/w
print ('root lies b/w', x_start,'and',x_start+dx)
break
else:
x_start=x_start+dx
i=i+1
if i==2000:
print ('root does not lie b/w zero and',x_start+i*dx)
## it is algorithm in python
