Solving nonlinear function using fzero, Error Function values at the interval endpoints must differ in sign.

```

Imp=100;
t0=1e-6;
P=204000000;
Tf=2e-3;
x = fzero( @(x) myfunction(x, t0, Imp, P, Tf), [1.001, 10000]);
function [f] = myfunction( x, t0, Imp, P0, Tf)
f = Imp - (-(P0*t0*(x-1.0)*(x^(-Tf/(t0*(x-1.0)))-1.0))/(log(x)*(x^(-1.0/(x-1.0)) -x^(-x/(x-1.0))))+(P0*t0*(x^(-(Tf*x)/(t0*(x-1.0)))-1.0)*(x-1.0))/(x*log(x)*(x^(-1.0/(x-1.0))-x^(-x/(x-1.0)))));
end

```

x must bigger than 1.0

I don't think these input will make fzero suffer

thank you

[Sam Chak]

Please display the super long equation in LaTeX mark-up.

This helps to check the parentheses in the MATLAB code.

[Walter Roberson]

The function is continually negative over that range.

[Walter Roberson]

It is +100 at x=-1 but change x away from -1 and it goes complex, so at the moment I have no evidence that it has a real root.

[Sam Chak]

@Miraboreasu

Once you have found the root of nonlinear function, can you verify if the solution really crosses 0?

Imp = 100;
t0  = 1e-6;
P0  = 204000000;
Tf  = 2e-3;
f   = @(x) Imp - (-(P0*t0*(x-1.0)*(x^(-Tf/(t0*(x-1.0)))-1.0))/(log(x)*(x^(-1.0/(x-1.0)) -x^(-x/(x-1.0))))+(P0*t0*(x^(-(Tf*x)/(t0*(x-1.0)))-1.0)*(x-1.0))/(x*log(x)*(x^(-1.0/(x-1.0))-x^(-x/(x-1.0)))));

Answer 1

[Lateef Adewale Kareem]

Imp=100;
t0=1e-6;
P=204000000;
Tf=2e-3;

x = nan;
options = optimset('Display','off'); % show iterations
x0 = 2;
while(isnan(x))
    x = fzero( @(x) myfunction(x, t0, Imp, P, Tf), x0, options);
    x0 = x0*1.2;
end
disp(['x = ', num2str(x)])

x = 1.762566874060497e+21

function [f] = myfunction( x, t0, Imp, P0, Tf)
    f = Imp - (-(P0*t0*(x-1.0)*(x^(-Tf/(t0*(x-1.0)))-1.0))/(log(x)*(x^(-1.0/(x-1.0)) -x^(-x/(x-1.0))))+(P0*t0*(x^(-(Tf*x)/(t0*(x-1.0)))-1.0)*(x-1.0))/(x*log(x)*(x^(-1.0/(x-1.0))-x^(-x/(x-1.0)))));
end