function alpha = lagrange_search(f_a, low, max)

a = linspace(low, max, 3);

f1 = f_a(a(1));

f2 = f_a(a(2));

f3 = f_a(a(3));

% gama_1 = @(a) (a - a(2))*(a - a(3))/((a(1)- a(2))*(a(1) - a(3)));

% gama_2 = @(a) (a - a(1))*(a - a(3))/((a(2)- a(1))*(a(2) - a(3)));

% gama_3 = @(a) (a - a(1))*(a - a(2))/((a(3)- a(1))*(a(3) - a(2)));

%

% q = @(a) f1*gama_1(a) + f2*gamma_2(a) + f3*gamma_3(a);

res = (f1*(a(2) + a(3))/((a(1) - a(2))*(a(1) - a(3))) + ...

f2*(a(1) + a(3))/((a(2) - a(1))*(a(2) - a(3))) + ...

f3*(a(1) + a(2))/((a(3) - a(1))*(a(3) - a(2)))) / ...

(f1*2/((a(1) - a(2))*(a(1) - a(3))) + ...

f2*2/((a(2) - a(1))*(a(2) - a(3))) + ...

f3*2/((a(3) - a(1))*(a(3) - a(2))));

if (res >= low) && (res <= max)

alpha = res;

else

if(f1 > f2)

alpha = a(1);

else

alpha = a(2);

end

end