Gaussian derivatives

Generate Gaussian kernels for a given scale "sigma", and display the kernel.

The size of the kernel should be floor(3*sigm)+1;

(i) Write an m-file "gauss.m" which generates Gaussian kernel.

function G=gauss(sigm)
s=floor(3*sigm)+1;
x=[-s:s];
G = exp(-x.^2/(2*sigm^2));
G=G/sum(sum(G));
plot(?);

Why G has to be normalized?

(ii) write an m-file gauss_x.m which generates 1 order derivative of the Gaussian kernel.

function G=gauss_x(sigm)
s=floor(3*sigm)+1;
x=[-s:s];

G=?

(iii)  Write an m-file gauss_xx.m which generates 2 order derivative of the Gaussian kernel.

function G=gauss_xx(sigm)
s=floor(3*sigm)+1;
x=[-s:s];
G=?

Observe Gaussian kernels for different sigma values.
Why the size of the kernel should be  (3*sigm)+1 ?