because NaN or Inf function value encountered during search while using fzero

I have a nonlinear equation---5e6-5e6*(exp(-aa*xt)-exp(-bb*xt))/(exp(-aa*1e-6)-exp(-bb*1e-6))=0

I am thinking is that due to the function is too nonlinear, and fzero cannot find the result?

For reference, the results should be 1e-6

aa=810930;
bb=1216395;
func = @(xt) 5e6-5e6*(exp(-aa*xt)-exp(-bb*xt))/(exp(-aa*1e-6)-exp(-bb*1e-6));
x0 = 0.00001;
roots = fzero(func,x0)

Exiting fzero: aborting search for an interval containing a sign change
    because NaN or Inf function value encountered during search.
(Function value at -0.0008092 is Inf.)
Check function or try again with a different starting value.

roots = NaN

Answer 1

[Matt J]

The problem occurs because func() has no axis crossing.

aa=810930;
bb=1216395;
func = @(xt) 5e6-5e6*(exp(-aa*xt)-exp(-bb*xt))/(exp(-aa*1e-6)-exp(-bb*1e-6));
x0 = 0.00001;

fplot(func,[0,10e-6])

Based on the plot, it appears you should be looking for the minimum of func() rather than a root.

xmin=fminsearch(func,x0)

xmin = 1.0000e-06