fi=[-1,2,0,-1,3];
gi=inline("i*i*log(2*i+1)+(i^2)/(i+1)");
i=3;
z=0.1;
i1=i+z;
i2=i-z;
disp("t(i)= -i^4 + 2*i^3 - i + 3");
disp("Pierwsza pochodna");
tp = (polyval(fi,i1)-polyval(fi,i2))/(2*z);
disp(tp);
disp("Sprawdzenie");
disp(polyval(polyder(fi),i));
disp("Druga pochodna ");
tpp = (polyval(fi,i1)+polyval(fi,i2)-2*polyval(fi,i))/z^2;
disp(tpp);
disp("Sprawdzenie");
disp(polyval(polyder(polyder(fi)),i));
disp("-------------------------------------------------------------------------");
disp("k(i)= 3*i*log(2*i + 1) + (i^2)/(i+1)");
disp("Pierwsza pochodna");
disp((gi(i1)-gi(i2))/(2*z));
disp("Sprawdzenie");
disp("k'(i)= -i^2/(1 + i)^2 + (2*i)/(1 + i) + (6*i)/(1 + 2*i) + 3*log(1 + 2*i)");
kp = -i^2/(1 + i)^2 + (2*i)/(1 + i) + (6*i)/(1 + 2*i) + 3*log(1 + 2*i);
disp(kp);
disp("Druga pochodna ");
disp((gi(i1)+gi(i2)-2*gi(i))/z^2);
disp("Sprawdzenie");
disp("k''(i) = (2*(6*i^4 + 24*i^3 + 40*i^2 + 28*i + 7))/((1 + i)^3 * (1 + 2*i)^2)");
kpp = (2*(6*i^4 + 24*i^3 + 40*i^2 + 28*i + 7)) / ((1 + i)^3 * (1 + 2*i)^2);
disp(kpp);
disp("(5*(t''(i) - k''(i))^2 + 10) / ((t'(i)+k'(i))^2 + 1)");
disp((5*(tpp - kpp)^2 + 10) / ((tp+kp)^2 + 1));