Do you need to know how to find those points given the raw data in a single vector array? If so, see approach below.
Find the slope by finding the difference from the left and then take the absolute value. Find the slopes (datapoints) that are greater than a specific threshold. Note, if you only care about the positive slope (the two red points to the left in the example you provided) then do not take the absolute value. Do the same thing coming from the right. Find the identified datapoints that are common between the left and right approach.
x = 1:11;
y = [0 0 0 0.3 0.8 1 1 1 0.5 0 0];
figure
scatter(x,y,'filled')
threshold = 0.1;
x1 = x(2:end);
y1 = abs(diff(y));
x_left = x1(y1>threshold)
x2 = flip(x(1:end-1));
y2 = abs(diff(flip(y)));
x_right = x2(y2>threshold)
values = intersect(x_left,x_right)
figure
scatter(x,y,'filled')
hold on
scatter(values,y(values),'filled','r')
Approached shown with visualizations:
figure
scatter(x,y,'filled')
Approach from the left
figure
x1 = x(2:end);
y1 = abs(diff(y));
x_left = x1(y1>threshold)
scatter(x1,y1,'filled')
Approach from the right
figure
x2 = flip(x(1:end-1));
y2 = abs(diff(flip(y)));
x_right = x2(y2>threshold)
scatter(x2,y2,'filled')
Find the values in common between x_left and x_right.
values = intersect(x_left,x_right)
figure
scatter(x,y,'filled')
hold on
scatter(values,y(values),'filled','r')
