How to stimulate an FM modulator?

 For an assignment I've got to stimulate an FM modulator I did that part
But I need help to find the "MINIMUM MODULATOR INDEX WHEN THE POWER OF THE CARRIER FREQUENCY IS REDUCED TO ZERO(BELOW 0.01)" 
here is the code which I did.

%code bigins

close all;

clear all;

fc = 100;%carrier frqncy

Fs = 1024;%sampling rate

fm=1;%modulating frqncy

Ts=1/Fs;%sample period

t=[0:Ts:120];%observation period

m=cos(2*pi*fm*t);%modulating signal

beta=0.5;%modulating index

theta=2*pi*fc*t+2*pi*beta*cumsum(m)*Ts;%integral signal

s=cos(theta);

FFTsize =4096;

S=spectrum(s,FFTsize);%s(401) is the power of the carrier

Freq=[0:Fs/FFTsize:Fs/2];

subplot(2,1,1),plot(t,s),xlabel('Time(ms)'),ylabel('Amplitude');

axis([0 0.5 -1.5 1.5]),grid on

subplot(2,1,2),stem(Freq,sqrt(S/682))

xlabel('Frequency (kHz)'),ylabel('Amplitude Spectrum');

axis([95 105 0 1]),grid on

for i = 0:5;

betai = i;

thetai=2*pi*fc*t+2*pi*betai*cumsum(m)*Ts;%integral signal

si=cos(thetai);

FFTsize =4096;

Si=spectrum(si,FFTsize);%s(401) is the power of the carrier

Freq=[0:Fs/FFTsize:Fs/2];

figure;

stem(Freq,sqrt(Si/682)); axis([99.9 100.1 0 1.05]);

end

%code is over

By using the code I got the power of carrier frequency when the modulation index is 0,1,2,3,4 and 5 in six different figures(that's what the code does).
What i want to do is to plot the data I've got from those six different figures in a same modulation index(X-axis) vs power of carrier frequency(Y-axis) graph.
Thank you in advance