fzero returns complex result

Hi,

I am running this code

f4=@(x) 0.1*0.4*(0.1*x+100)^(-0.8)-0.1*0.5*(-0.1*x+100)^(-0.8)+0.5*0.1*(0.5*x+100)^(-0.8);
fzero(f4,3)

and it only returns my NaN

Exiting fzero: aborting search for an interval containing a sign change because complex function value encountered during search. (Function value at -230.705 is -0.0043742-0.0033056i.) Check function or try again with a different starting value.

ans =

   NaN

But if I change that the start poin to 200 I can get the result I want which is 225.3938. My question is how can I get the real root in general case? Before I get the solution I can't tell where is it so I can't choose a proper start point. I can't just randomly try different start points every time when I solve a function like this...

Answer 1

[Walter Roberson]

Analyze the parts of your expression. You have

(-0.1*x+100)^(-0.8)

That is going to go complex if (-0.1*x+100) < 0, which is x > 1000. Likewise analyze the other subexpressions. You will be able to establish an upper and a lower bound on when the function goes complex. Then use the interval x0 form of fzero

fzero(f4, [-31415926, 2718285])   %for example

[xueqi]

I need to pass different parameters to functions I want to solve so I can't do these analysis. Is there any routine can solve it automatically? I tried to use Maple. And if I use 'solve' it gives me the same complex result while 'fsolve' gives me the solution which is real. So I think in matlab there must be the same alternative routine.

[xueqi]

Any other suggestion please?