Debugging construction of splines between a variable amount of points - matlab

Question

Given an amount of points in x and y I want to create splines that intersect all points and that have the same slopes in intersections.
My approach has been to establish a set of equations for intersection of points as well as dictating equal slopes at intersections and then use fsolve() to determine coefficients.
However, when plotting the found splines they do not have the same slopes at intersecting points though they do intersect the correct points given in x and y.
I have been trying to debug this script for most of two days now without any luck. Can someone point out why my splines are not getting the correct slopes? Or can it be that fsolve() quits before a satisfactory solution has been found?
Main file:
result = fsolve(#(K) eqns(x,y,K) , ones(1,(size(x,1)-1)*3) ); %Calls eqns() in eqns.m
A = result(1 : size(x,1)-1 );
B = result(size(x,1) : 2*size(x,1)-2 );
C = result(2*size(x,1)-1 : 3*size(x,1)-3 );
%Plot splines
splinePts = size(A,2)*100;
x_spline = [0 : x(end)/splinePts : x(end)];
fx = ones(splinePts,1);
for i = 1:size(A,2)
for j = 1:100
k = i*100-100 + j;
fx(k) = A(i) * x_spline(k)^2 + B(i) * x_spline(k) + C(i);
end
end
plot(fx);
eqns.m
function fcns=eqns(x,y,K)
A = K(1 : size(x,1)-1 ); %Coefficients for X^2
B = K(size(x,1) : 2*size(x,1)-2); %Coefficients for X
C = K(2*size(x,1)-1 : 3*size(x,1)-3); %Constants
%Equations for hitting all points
syms H;
temp = H; %Initiate variable for containing equations.
for i = 1:size(B,2)
temp(end+1) = eqn(x(i),y(i),A,B,C,i); %Calls eqn() in eqn.
temp(end+1) = eqn(x(i+1),y(i+1),A,B,C,i);
end
%Equations for slopes at spline intersections
syms X;
temp(end+1) = subs( diff(eqn(X,0,A,B,C,1),X) - 0 , 'X' , x(1) );
for i = 1:size(A,2)-1
temp(end+1) = subs( diff(eqn(X,1,A,B,C,i),X) - diff(eqn(X,1,A,B,C,i+1),X) , 'X' , x(i)+1 );
end
fcns = double( temp(2:end) );
end
eqn.m
function fcn=eqn(X,Y,A,B,C,i)
fcn = A(i)*X^2 + B(i)*X + C(i) - Y;
end