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## fsolve fails to find a zero of a non-linear function, while the plot displays a zero

Hi there,

fsolve fails me, for the first time. I have this very messy expression, which comes out of a cubic equation. It must have a zero. I plot it and the graph, smooth, shows a zero between 16.4 and 16.5, but maple's fsolve fails to find it, why's that? The slope of the function is very flat near the zero. I tried to tell maple the solution is between 16.4 and 16.5, to no avail.

Any advice will be much appreciated. The following code tells it all.

many thanks,

Patrick.

> restart: with(plots):
> Q:= x-> (.5/x^.5-.12)*(.15-.5/x^.5)+(.5/x^.5-.135)*(.8333333333e-3/x^2*(-4460700.*x^(11/2)+200197.*x^6+36840000.*x^5-82000000.*x^(9/2)+207.8460969*(535279.*x^12-23652435.*x^(23/2)+449152175.*x^11-4419860000.*x^(21/2)+.2225093750e11*x^10-.4308750000e11*x^(19/2)-3125000000.*x^9)^(1/2))^(1/3)+.8333333333e-3*(2569.*x^4-38600.*x^(7/2)+190000.*x^3)/x^2/(-4460700.*x^(11/2)+200197.*x^6+36840000.*x^5-82000000.*x^(9/2)+207.8460969*(535279.*x^12-23652435.*x^(23/2)+449152175.*x^11-4419860000.*x^(21/2)+.2225093750e11*x^10-.4308750000e11*x^(19/2)-3125000000.*x^9)^(1/2))^(1/3)-.8333333333e-3*(-500.*x^(3/2)+107.*x^2)/x^2): Q(x):
> xss:=fsolve(Q(x)=0, x=0..25, complex): xss:
> p:=plot({Q(x)}, x=0..25):  display(p,view=[0..25,-0.3..0.3]);
> interface(displayprecision=12):
> evalf(Q(16.4)); evalf(Q(16.5));
> fsolve(Q(x)=0, x=16.4..16.5);

﻿