MATLAB: Locating point on x-axis where the slope is decreasing

decreasingindexMATLABslopesteepest

Dear all,
I used the following code to plot the angle over time:
figure
hold on
grid on
plot(Time, theta,'linewidth',1.5)
xlabel('Time [s]','FontWeight','bold')
ylabel('\theta [deg]','FontWeight','bold')
xlim([0 round(Time(end))])
legend('Opening angle','Location','northeast')
title('Opening angle')
The resulting graph is shown below. I want to index at what time the slope is decreasing. How can I do that?
The variables Time and theta to plot this graph can be found in the data.mat file.

Best Answer

A reasonably robust way is to use the ischange function: 
D = load('data.mat');
Time = D.Time;
theta = D.theta;
[TF,m,b] = ischange(theta, 'linear', 'Threshold',5);
chgpts = [find(TF); m(TF); b(TF)].';
chgidx = find(chgpts(:,2)<0,1);
figure
plot(Time, theta,'linewidth',1.5)
hold on
plot(Time(chgpts(chgidx(:,1))), theta(chgpts(chgidx(:,1))), 'xr')
hold off
grid on
xlabel('Time [s]','FontWeight','bold')
ylabel('\theta [deg]','FontWeight','bold')
xlim([0 round(Time(end))])
legend('Opening angle','Location','northeast')
title('Opening angle')
producing:
The ‘Time’ value is then: 
ChangePointTime = Time(chgpts(chgidx(:,1)));
that here is 6.01 seconds.
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