So I assume you have the red, fitted curve since you plotted it (if not see first 2 lines below), so why can't you just simply do
coefficients = polyfit(x, y, 4); % fit to a 4th order polynomial.
yfit = polyval(coefficients, x); % Evaluate the fit at the same x values.
minFit = min(yFit); % Find min of fitted curve in the range we have fit it over.
maxFit = max(yFit); % Find max of fitted curve in the range we have fit it over.
If you want, you can use an x in polyval() that has finer resolution than the original x. Something like
numSamplePoints = 2000; % However many you need to get the resolution you want.
xFit = linspace(min(x), max(x), numSamplePoints);
yfit = polyval(coefficients, xFit); % Evaluate the fit at the same x values.
Of course you could get the exact value of the apex just by computing the derivative from the coefficients vector.
