Try this -
%%// Min-max index ranges
min_ind_range = [20 50];
max_ind_range = [50 100];
%%// Min value
[minVal, minIndex] = min(x(min_ind_range(1):min_ind_range(2)));
minIndex = minIndex+min_ind_range(1)-1
%%// Max value
[maxVal, maxIndex] = max(x(max_ind_range(1):max_ind_range(2)));
maxIndex = maxIndex+max_ind_range(1)-1
Edit 1: For a number of data as is the case with the upper two graphs, use this -
%%// Min-max index ranges
min_ind_range = [20 50];
max_ind_range = [50 100];
%%// *** Left Case ***
%%// Min value
[left_minVal, left_minIndex] = min(left_data(min_ind_range(1):min_ind_range(2),:));
left_minIndex = left_minIndex+min_ind_range(1)-1;
[left_maxVal, left_maxIndex] = max(left_data(max_ind_range(1):max_ind_range(2),:));
left_maxIndex = left_maxIndex+max_ind_range(1)-1;
%%// *** Right Case ***
%%// Min value
[right_minVal, right_minIndex] = min(right_data(min_ind_range(1):min_ind_range(2),:));
right_minIndex = right_minIndex+min_ind_range(1)-1;
[right_maxVal, right_maxIndex] = max(right_data(max_ind_range(1):max_ind_range(2),:));
right_maxIndex = right_maxIndex+max_ind_range(1)-1;
Please note that now we have a series of min-max values and their indices.