You could do this in Javascript.
data = $.getJSON("https://api.thingspeak.com/channels/XXXXXX/feeds.json?days=1");
var maxVal = -Infinity;
for (var i = 0; i < data.feeds.length; i++) {
if (data.feeds[i].field1 > maxVal) {maxVal = data.feeds[i].field1;}
}
maxVal should have the maximum value of field1 in the last day (assuming you have accumulated <8000 points) in the last day.