simple False Position code

I'm trying to do a simple False Position code following my teachers model but can't get it to actually work. Not sure if my if, else is wrong or what as it only says Method failed but I know there should be and answer of P=3.0571 and i=16. Totally new to programming and matlab so any help would be greatly valued. Thanks

%False Position %(x^2-4x+4-lnx=0 for 2<=x<=4)

p0=2; p1=4; TOL=10^-6; N=100;

q0=p0^2-4*p0+4-log(p0); q1=p1^2-4*p1+4-log(p1);

i=2; while i<=N p=p1-q1*(p1-p0)/(q1-q0);

    if abs(p-p1)<TOL
        disp('False Position')
        p
        i
        break
    end

     i=i+1;
    q=p^2-4*p+4-log(p);

    if q*q1<0
        p0=p1;q0=q1;
    else
        p1=p;q1=q;
    end
end

   if i>=N disp('Method Failed')
   end

Answer 1

[Roger Stafford]

I believe your error lies in the lines

if q*q1<0
  p0=p1;
  q0=q1;

They ought to read

if q*q1<0
  p0=p;
  q0=q;

The idea is to keep the signs of q0 and q1 opposite, so you set either (p1,q1) or (p0,q0) to (p,q) whichever will retain that as true while continually shrinking the interval length. You were setting (p0,q0) to (p1,q1) which would suddenly shrink the interval length to zero with the true solution off to one side.