Matlab Function fzero and Error using fzero (line 273)

Hello Guys!

I'm Kinda new to matlab, so be gentle with me!

Im doing my homework for my university, and while i was writing the code and using fzero function, it gaves me this error ( not a the first zeroes i want to know but at the second ) :

Error using fzero (line 273) The function values at the interval endpoints must differ in sign.

im calculating two different zeroes ( one and two ) of a referement function of my own.

ill post here the code to be more clear :

-----

Function :

funref = @(x) 2.7*(1./(1+5*(x-1).^2))+4.52*(1-(2*exp(x))./(1+5*x.^2));

---

Graph :

x = linspace(-1,2);
plot(x,funref(x),[-1,2],[0,0], ':r')

hold on 

text (-0.53,0, 'first zero');

text (0.55, 0, 'Second Zero');

text (0.2,-4.4, 'Minimum' );

text (1.2, 3.25, 'Maximum');

axis ([-1 2 -5 5]);

y = linspace(-5,5);

line([0.091 0.091],[y(1),y(end)], 'lineWidth', 1);
text (0.1, 4, 'Minimum abscissa');

line([1.08 1.08], [y(1),y(end)], 'lineWidth', 1);
text (1.1, -2, 'Maximum abscissa' );

--- Zeroes Approximation :

firstzero = fzero(funref,[-0.53,0])

-- AND HERE I GOT THE DAMN PROBLEM : --

secondzero = fzero(funref,[0.55,0])

Here it gave me the error :

Error using fzero (line 273)
The function values at the interval endpoints must differ in sign.

im driving crazy, i really dont know where im mistaking.

Please help me! Thank you a lot.

[Walter Roberson]

By the way, notice you reversed the 0 and 0.55 in your second call. That would not have caused the problem you are observing though.

Answer 1

[Steven Lord]

Add two circles to your plot, indicating the endpoints of the interval over which your second fzero call is searching for a zero.

funref = @(x) 2.7*(1./(1+5*(x-1).^2))+4.52*(1-(2*exp(x))./(1+5*x.^2));
x = linspace(-1,2);
plot(x,funref(x),[-1,2],[0,0], ':r')
hold on;
plot([0, 0.55], funref([0, 0.55]), 'ko')

Now do you see the problem? If the value of your function at the two endpoints has the same sign, you may not have a solution on that interval and so fzero says it's not going to search for something it's not sure exists. [Granted, there are intervals where the two endpoints have the same sign but there are multiple zeros inside the interval, like if you'd asked for a zero on the interval [-1, 1]. This is a limitation of fzero with the interval syntax.]

If you stretch your interval slightly, to something like [0 0.6], you'll find that second zero.