MATLAB: Fzero not working (thanks in advance for help)

fsolve

unction file
    function y = f(x,a,A,b,Ttx,gamma_b)
    y = ((a./A)-(((1+gamma_b)/2)*(b./Ttx)));
    end
script and error
>> xVec=0:0.01:0.4;  %axial combuster length (can be varied according to user input and units)
xi=xVec(1);  %station 3 (combuster starting point)
x4=xVec(end);%station 4 (combuster end point)
gamma_b=1.36;%Average value of ratio of specific heat capacities during burning
gamma_c=1.4;%Average value of ratio of specific heat capacities during compression
X=((xVec-xi)/(x4-xi));
a3=0.0038;%station 3 cross secion area in m2.
A=a3*(1+X);%Area Profile
a=gradient(A,xVec);%dA/dx in equation (6-90)
a1Vec=a./A; %(dA/dx)/A in equation (6-90)
tau_b=1.5; %Tt4/Tt2 in eq. (6-91) overall total temerature rise in burner
theta=2;%emperical constant in eq. (6-91)
Tt2=2200;%Total temperature at station 2 depends on inlet and compression conditions (USER SPECIFIED)
Ttx=Tt2*(1+(tau_b-1)*((theta*X)./(1+(theta-1)*X)));%Temperature profile eq. (6-91)
b=gradient(Ttx,xVec);%dTt/dx in equation (6-90)
b1Vec=b./Ttx;%(dTt/dx)/Tt in equation (6-90)
fun = @f; % function
x0 = 0; % initial point
z = fzero(fun,x0);
Error using fzero (line 289)
FZERO cannot continue because user supplied function_handle ==> f failed with the error below.
   Not enough input arguments.

Best Answer

Assuming that you are trying to find x such that the equation you posted to Star Strider is satisfied, there are two ways to do what you want. The first is essentially a brute-force numerical minimization. Since you've computed the area, temperature field, and respective derivatives numerically, you can just take the absolute minimum of the function and use that X-value as your solution. Assuming the script posted above, you can write:
fun = @(x)((a./A)-(((1+gamma_b)/2)*(b./Ttx))); % Function of x only
[fMin, idx] = min(abs(fun(X)));
xMin = X(idx);
% Verify with plot
plot(X, fun(X), xMin, fMin, 'o');
For better resolution, just reduce the step size in 'xVec.' (If I used the wrong variables above, I hope you still get the idea).
Your other option is to write out the analytical values and derivatives for A, dA/dx, Tt, and dTt/dx. Then, incorporate them all into the function so that it a function of X only. Fzero will work for you then. If you give it numerical derivatives, as you're doing here, there's no way it can zero the function for you.
You could also look into ode45 but that's probably more trouble than it's worth.
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