how can I use my function f to replace a and b with writing all the equation every time? x^3 + a^2*x^2 - 10)*sin(x) - y) like f(a)*f(b)<0

clc;
clear;
syms p;
x = 13.61015;
y = 13257;
a = 5.14;
b = 11.47;
err1 = 0.000001;
f = (x^3 + p^2*x^2 - 10)*sin(x) - y == 0;
i=0;

 if ((x^3 + a^2*x^2 - 10)*sin(x) - y) * ((x^3 + b^2*x^2 - 10)*sin(x) - y) > 0
    disp ('Wrong Interval');
    return
 end

Answer 1

[Torsten]

x = 13.61015;
y = 13257;
a = 5.14;
b = 11.47;
err1 = 0.000001;
f = @(x,y,p) (x^3 + p^2*x^2 - 10)*sin(x) - y ;
f(x,y,a)

ans = -6.8568e+03

f(x,y,b)

ans = 9.9765e+03

[Nikolas]

thank you for your help

[Torsten]

So you have two points a, b with f(a)*f(b) < 0.

Now you will form c = (a+b)/2 and calculate f(a)*f(c) and f(b)*f(c).

If f(a)*f(c) < 0, you will set a = a and b = c.

If f(b)*f(c) < 0, you will set a = c and b = b.

And continue in the same way for the next step.