You should now be familiar with MATLAB's built-in "max" function. Without using the built-in max(), min() and sort() functions, write a function that takes vector as an input and returns the maximum value as well as the index at which the maximum value occurs. Your function should work with input vectors of any length. Your function header should be similar to the following: function [max value, index] = mymax(x)
Test your function for f(x)=x ^(1/x) for x values between 0 and 50 with a step size of 0.001. Check the maximum value and index using MATLAB's built-in max() function. Plot f(x) and mark the maximum point. Remember to include a legend.