Finding domain and range with polyfit/polyval

I have coefficients to an 17th order polynomial that fits my data well. When I zoom into the graph from y=0 to y=15 this is what I see. I want MatLab to tell me the time it takes the top curve to go from y=0 to y=15.

Someone told me to use polyval(coef,15) - polyval(coef,0) But that gave me 5.9235e+09 when it should be something like 3.8 seconds.

Answer 1

[Matt J]

In theory, you would do,

[c1,c2]=deal(coef);
c2(end)=c2(end)-15;

r1=roots(c1);
r2=roots(c2);

time=r2(r2>43 & r2<45) - r1(r1>37 &r1<39);

However, in practice, root finding operations for polynomials of super-high order are mumerically unstable, see

https://en.wikipedia.org/wiki/Wilkinson%27s_polynomial