Error exercise roots of the bessel function

Could someone help me find the mistake I am making?

The exercise is as follows:

My code is the following:

I don't know why my root values of the Bessel function are bad.

[Walter Roberson]

The order of r does not appear to be ascending to me.

[Cristian Segura Bidermann]

How should the values be then?

[Walter Roberson]

You assign to r(6) first using 4 as the starting approximation. If everything goes well, you will get the root that is close to 4.

You assign to r(5) second using 7 as the starting approximation. If everything goes well, you will get a root that is close to 7. If all went well, this root will be after the root that was near 4, so it should be after the one for 4 in the r vector. But you stored it into r(5) which will be before the one for 4 in the r vector.

Why are you storing into r(6) then r(5) then r(4) ?