Hello Dylan,
To evaluate and display specific y-values for the first and second derivatives of a spline at given x-values, you can use the fnval function to compute these values. Then, you can display the results using fprintf or annotate them directly on your plot. Here is a step-by-step guide on how to modify your code to achieve this:
- Define Specific x-values: Decide which specific x-values you want to evaluate.
- Evaluate the Derivatives: Use fnval to compute the values of the first and second derivatives at these specific x-values.
- Display the Results: Use fprintf to print the results or annotate them on the plot.
Here is how you can modify your code:
close all;
% Define data points
x = linspace(-3, 3, 9);
y = [2, 3, 4.1, 4.5, 2, 2, 3, 3, 3];
% Define a finer grid for plotting the spline
xx = linspace(-3, 4, 100); % Use more points for smoother plots
% Compute the spline
pp = spline(x, y);
% Evaluate the spline and plot it
yy = ppval(pp, xx);
plot(x, y, '.', 'markersize', 10);
hold on;
plot(xx, yy, 'b');
% Compute and plot the first derivative
dpp = fnder(pp);
plot(xx, fnval(dpp, xx), 'k');
% Compute and plot the second derivative
ddpp = fnder(dpp);
plot(xx, fnval(ddpp, xx), 'r');
% Define specific x-values for evaluation
specific_x_values = [-2, 0, 2]; % Example x-values
% Evaluate and display the derivatives at specific x-values
for i = 1:length(specific_x_values)
x_val = specific_x_values(i);
y_val = fnval(pp, x_val);
dy_val = fnval(dpp, x_val);
ddy_val = fnval(ddpp, x_val);
fprintf('At x = %.2f, f(x) = %.4f, f''(x) = %.4f, f''''(x) = %.4f\n', x_val, y_val, ...
dy_val, ddy_val);
% Annotate the plot
plot(x_val, dy_val, 'ko', 'MarkerFaceColor', 'k'); % First derivative
plot(x_val, ddy_val, 'ro', 'MarkerFaceColor', 'r'); % Second derivative
text(x_val, dy_val, sprintf('%.2f', dy_val), 'VerticalAlignment', 'bottom', ...
'HorizontalAlignment', 'right');
text(x_val, ddy_val, sprintf('%.2f', ddy_val), 'VerticalAlignment', 'bottom', ...
'HorizontalAlignment', 'right');
end
hold off;
The output you get looks like:
I hope this helps!
