Programming a function which is able to display Maximum or Minimum of an 1-dimensional function

edit

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?