My error says "Unrecognized function or variable 'CP'." What can I add to the script so that I can define it?

%Use symbolic processing with the variable x
syms x

%Enconde the function f(x)
f(x) = (1-x^2)/(1+x^2)

%Set the distance to the left/right of the critical point
h=0.01

%Find the first derivative of the function
 fp(x) = diff(f,1);

%Solve for the roots of fp
root1 = solve(fp)

%Consider the first critical point only
c=root1(1)

%Determine if the function is "Increasing" or "Decreasing" at the right of the critical point
if (fp(c+h)>0)
    IoDR = "Decreasing"
elseif (fp(c+h)<0)
    IoDR = "Increasing"
end

%Determine if the function is "Increasing" or "Decreasing" at the right of the critical point
if (fp(c-h)>0)
    IoDL =  "Increasing"
elseif (fp(c-h)<0)
    IoDL =  "Decreasing"
end

%Use first derivative Test to Determine if the critical point is a "Maximum" point or "Minimum" point.
if IoDL=="Increasing" & IoDR =="Decreasing"
    cp(x)= "Minimum"
elseif IoDL=="Decreasing" & IoDR =="Increasing"
    cp(x)= "Maximum"
end

%Find the second derivative of the function
fpp(x)= diff(f,2);

%Find the points of inflection of the function by equating the second derivative of the function to zero.
cc = (-sqrt(3)/3), (1/2)
     (sqrt(3)/3), (1/2)

%Apply Second Derivative Test to check whether the critical point is a "Maximum" point, a "Minimum" point or "Point of Inflection".
if fpp(c) >0
    cp2 = "Minimum"
elseif fpp(c)<0
    cp2 = "Maximum"
else
    cp2 = "Point of Inflection"
end


%GRAPH THE FUNCTION
clf();
g1= ezplot(f);
hold on
grid on
plot(c,f(c), 'r*')
title("Curve Tracing")
text(c+.5,f(c),["("+string(c)+","+string(f(c))+")   "+CP  ])

Answer 1

[VBBV]

None of the if statements for variables IoDR, IoDL are being executed. Can you check if the preceding if conditions for variable fp are correct ? As you can see below, IoDR & IoDLare both "increasing", which makes the variable CP undefined

%Use symbolic processing with the variable x
syms x

%Enconde the function f(x)
f(x) = (1-x^2)/(1+x^2)

f(x) = 

%Set the distance to the left/right of the critical point
h=0.01

h = 0.0100

%Find the first derivative of the function
 fp(x) = diff(f,1);

%Solve for the roots of fp
root1 = solve(fp)

root1 = 

0

%Consider the first critical point only
c=root1(1)

c = 

0

%Determine if the function is "Increasing" or "Decreasing" at the right of the critical point
if (fp(c+h)>0)
    IoDR = "Decreasing"
elseif (fp(c+h)<0)
    IoDR = "Increasing"
end

IoDR = "Increasing"

%Determine if the function is "Increasing" or "Decreasing" at the right of the critical point
if (fp(c-h)>0)
    IoDL =  "Increasing"
elseif (fp(c-h)<0)
    IoDL =  "Decreasing"
end

IoDL = "Increasing"

%Use first derivative Test to Determine if the critical point is a "Maximum" point or "Minimum" point.
if IoDL=="Increasing" & IoDR =="Increasing"
    CP = "Minimum"
elseif IoDL=="Decreasing" & IoDR =="Decreasing"
    CP = "Maximum"
end

CP = "Minimum"

%Find the second derivative of the function
fpp(x)= diff(f,2);

%Find the points of inflection of the function by equating the second derivative of the function to zero.
cc = (-sqrt(3)/3), (1/2)

cc = -0.5774

ans = 0.5000

     (sqrt(3)/3), (1/2)

ans = 0.5774

ans = 0.5000

%Apply Second Derivative Test to check whether the critical point is a "Maximum" point, a "Minimum" point or "Point of Inflection".
if fpp(c) >0
    cp2 = "Minimum"
elseif fpp(c)<0
    cp2 = "Maximum"
else
    cp2 = "Point of Inflection"
end

cp2 = "Maximum"

%GRAPH THE FUNCTION
clf();
g1= ezplot(f);
hold on
grid on
plot(c,f(c), 'r*')
title("Curve Tracing")
text(c+.5,f(c),["("+string(c)+","+string(f(c))+")   "+CP  ])