Finding x value of local extrama

hello,

Below is my sample of code. In the code, Im taking a simple cos wave and transforming it to the frequency domain. Then, my goal is to find the fundamental frequency of that wave by examining the plot of the FFT.

I am able to find the magnitude of the peak (the y coordinate) in the FFT, however, I cant get the computer to spit out the x coordinate. In the example below, if max_x = 751, freq should equal 500.667. I can not produce the 751.

Thank you for your help, RC

clc; clear all; close all
fs = 50000 
t = 0 : 1/fs : 1.5-1/fs;
f1= 500;
x = cos(2*pi*f1*t);
plot(x);
title('inputed signal'); % title of figure
xlabel('Time'); % x-axis lable
ylabel('amplitude');  %y-axis lable 
%fourier transform of signal
X = fft(x);
%finding mag. information from signal 
y = abs(X);
figure (2);
plot(y);
title('Frequency Domain'); % title of figure
xlabel('Bins (related to freqency)'); % x-axis lable
ylabel('Magnitude');  %y-axis lable 
%finding peak y value in freqency domain
amp = max(y)
%finding coresponding bin value to that max
max_x = 
%relating the bin value to a freqency 
freq = (max_x * 50000)/ 7.5e4

Answer 1

[Guillaume]

The second return value of max is the index at which this maximum is found, so:

[map, max_x] = max(y)