lagrange plots

N=[1 10 100 1000 10000 100000 1000000];

x=log10(N);

p1=(x.^6-21*x.^5+175*x.^4-735*x.^3+1624*x.^2-1764*x+720)/720;
plot(x,p1,'y','LineWidth',1.25)

hold on

p2=-(x.^6-20*x.^5+155*x.^4-580*x.^3+1044*x.^2-720*x)/120;
plot(x,p2,'m','LineWidth',1.25)

p3=(x.^6-19*x.^5+137*x.^4-461*x.^3+702*x.^2-360*x)/48;
plot(x,p3,'c','LineWidth',1.25)

p4=-(x.^6-18*x.^5+121*x.^4-372*x.^3+508*x.^2-240*x)/36;
plot(x,p4,'r','LineWidth',1.25)

p5=(x.^6-17*x.^5+107*x.^4-307*x.^3+396*x.^2-180*x)/48;
plot(x,p5,'g','LineWidth',1.25)

p6=-(x.^6-16*x.^5+95*x.^4-260*x.^3+324*x.^2-144*x)/120;
plot(x,p6,'b','LineWidth',1.25)

p7=(x.^6-15*x.^5+85*x.^4-225*x.^3+274*x.^2-120*x)/720;
plot(x,p7,'--k','LineWidth',1.25)

title('\phii(x) plots')
xlabel('Number of stress cycles log10(N)')
ylabel('\phii(x)')
legend('\phi1(x)','\phi2(x)','\phi3(x)','\phi4(x)','\phi5(x)','\phi6(x)','\phi7(x)')