%% -----------Q7 part(a)---------------------------------------------------
f=@(x)sqrt(x) ;
a = 0 ; b = 1 ; c = 4 ;
x = [0 : 0.01 : 4] ;
p2 = (x-b).*(x-c).*f(a)/((a-b)*(a-c)) + (x-c).*(x-a).*f(b)/((b-c)*(b-a))...
    + (x-a).*(x-b).*f(c)/((c-a)*(c-b)) ;
figure(1) ;
plot(x,p2,'r') ;
hold on ;
fplot(f,[0 4]) ;
%% -----------Q7 part(b)---------------------------------------------------
f=@(x)log(x) ;
a = 1 ; b = 3/2 ; c = 2 ;
x = [1 : 0.01 : 2] ;
p2 = (x-b).*(x-c).*f(a)/((a-b)*(a-c)) + (x-c).*(x-a).*f(b)/((b-c)*(b-a))...
    + (x-a).*(x-b).*f(c)/((c-a)*(c-b)) ;
figure(2) ;
plot(x,p2,'r') ;
hold on ;
fplot(f,[1 2]) 
%% -----------Q7 part(c)---------------------------------------------------
f=@(x)log2(x) ;
a = 1 ; b = 2 ; c = 4 ;
x = [1 : 0.01 : 4] ;
p2 = (x-b).*(x-c).*f(a)/((a-b)*(a-c)) + (x-c).*(x-a).*f(b)/((b-c)*(b-a))...
    + (x-a).*(x-b).*f(c)/((c-a)*(c-b)) ;
figure(3) ;
plot(x,p2,'r') ;
hold on ;
fplot(f,[1 4]) ;
%% -----------Q7 part(d)---------------------------------------------------
f=@(x)sin(pi*x) ;
a = -1 ; b = 0 ; c = 1 ;
x = [-1 : 0.01 : 1] ;
p2 = (x-b).*(x-c).*f(a)/((a-b)*(a-c)) + (x-c).*(x-a).*f(b)/((b-c)*(b-a))...
    + (x-a).*(x-b).*f(c)/((c-a)*(c-b)) ;
figure(4) ;
plot(x,p2,'r') ;
hold on ;
fplot(f,[-1 1]) ;