Here is the code to perform the tasks mentioned:
```MATLAB
t = 0:3:24;
tempF = [42,40,39,44,53,56,51,45,43];
% Create a row vector tq with elements starting at 0 hour and ending at 24 hours with increments of 6 minutes (0.1 hour)
tq = 0:0.1:24;
% Compute interpolated temperature for the vector tq using the interp1 function with spline method
tempFq = interp1(t, tempF, tq, 'spline');
% Plot the result (tq vs tempFq) with the input (t, tempF)
plot(t, tempF, 'o');
hold on;
plot(tq, tempFq);
xlabel('Hr');
ylabel('Temperature (F)');
box off;
grid on;
% Find the maximum temperature and its time
[tempFmax, idx_max] = max(tempF);
tmax = t(idx_max);
% Find the minimum temperature and its time
[tempFmin, idx_min] = min(tempF);
tmin = t(idx_min);
```
Note: Make sure to run the code after defining the variables `t` and `tempF` as given in the question.