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I had to program a function today which is able to do what i wrote in the title. My attempt in doing this was that:

reset() forget() var('x') Extrempkt= {}

def g(f): f=f(x) f1(x)=diff(f(x),x); print(f1(x))

l=len(solve(f1(x)==0,x))
L=l-1;
A=[((solve(f1(x)==0,x)[n]).operands()[1]) for n in [0..L]]; print(A)

if n in [0..L]:
    if f1(A[n]-0.0000001)>f1(A[n]+0.0000001):
        Extrempkt.update({A[n]:"Maximum"})
    if f1(A[n]-0.0000001)<f1(A[n]+0.0000001):
        Extrempkt.update({A[n]:"Minimum"})

return (Extrempkt)

g((1/9)x^3-(1/3)x^2-(8/3)*x+9)

The problem is. My function only puts out my 2nd Extremum. Can you help me?

I had to program a function today which is able to do what i wrote in the title. My attempt in doing this was that:

reset()
forget()
var('x')
Extrempkt= {}
{}
  
def g(f):
    f=f(x)
    f1(x)=diff(f(x),x); print(f1(x))print(f1(x))
  
 l=len(solve(f1(x)==0,x))
 L=l-1;
 A=[((solve(f1(x)==0,x)[n]).operands()[1]) for n in [0..L]]; print(A)

 if n in [0..L]:
     if f1(A[n]-0.0000001)>f1(A[n]+0.0000001):
         Extrempkt.update({A[n]:"Maximum"})
     if f1(A[n]-0.0000001)<f1(A[n]+0.0000001):
         Extrempkt.update({A[n]:"Minimum"})

 return (Extrempkt)

g((1/9)*x^3-(1/3)*x^2-(8/3)*x+9)
 
g((1/9)x^3-(1/3)x^2-(8/3)*x+9) 
 
The problem is. My function only puts out my 2nd Extremum.
Can you help me?